Since you emphasize the word now in your question, I'll try to answer with an emphasis on the current escalation. For the more general question asking why there is a conflict at all, I'll simply refer to the Wikipedia article because it's such a complex issue that I cannot explain well.
So the questions I'll try to address are as follows:
I want to know why Gaza is being attacked now, who is attacking, and what they want.
Which parties are fighting?
The parties in conflict are the state of Israel and Hamas. The state of Israel has an advanced military, the IDF, that it uses to defend itself. Hamas is classified as a terrorist organisation by a number of countries (including the US, the EU and Israel), but it also controls the Gaza Strip.
What are the parties fighting for?
Hamas' aims are, according to Wikipedia:
Hamas, as its name (Islamic Resistance Movement) implies, aims to liberate Palestine from the Israeli occupation, and transform the country into an Islamic state. Which of these two objectives is the primary goal is disputed.
Israel is a state and its current military operations in the conflict are described as self defense. For example, in an interview with Face the Nation, Israeli PM Netanyahu said:
And I think any country has to defend itself. It has a natural right of self-defense. We'll do whatever it takes to restore order and quiet and the security of our people and deterrence. We're trying to degrade Hamas's terrorist abilities and to degrade their will to do this again.
I am not aware of any concrete demands that motivate the fighting in this current episode of violence.
This is the more interesting emphasis of your question. The previous answers are more general and could apply to previous escalations alike. One of the reasons the fighting has escalated as far as it has or has gone on for this long (Wikipedia's timeline for the current escalation starts on May 6th, though it considers heightened tensions in the weeks leading up to that) is political.
Specifically, on both sides of the conflict there are people in power who can use the escalation as a distraction from their own internal politics. As such, I'd argue that it's not just the events in the timeline that explain the lead up to the current level of violence. On both sides, the leadership has taken steps that are escalatory in nature, not aimed de-escalating the situation.
Continued war rhetoric from Israeli PM Netanyahu
Note that he isn't phrasing the military response as self-defense, instead he uses language of revenge ("levy a heavy price") and strength ("full force"). According to the Hindustan Times:
In a televised address, Netanyahu said Sunday evening the attacks were continuing at “full-force” and will “take time.“ Israel “wants to levy a heavy price” from Gaza’s militant Hamas rulers, he said, flanked by his defense minister and political rival, Defense Minister Benny Gantz, in a show of unity.
That rhetoric may seem insignificant but it's adding more oil to the fire. That directly benefits Hamas because it needs the perception of Israeli aggression to justify its actions and to remain popular with Palestinians.
Hamas setting an ultimatum that promises violence if not met
That's not a diplomatic request. Basically, it's setting up a justification for escalating further. According to nationalpost.com:
In Gaza, a Hamas spokesman said the leadership of a joint command of armed movements in the Palestinian enclave had given Israel “an ultimatum until 6 p.m. (1500 GMT)” to withdraw its security forces from the al Aqsa mosque compound and Jerusalem’s Sheikh Jarrah neighborhood.
Escalating won't resolve the conflict
We see that there's some escalating on both sides, but couldn't that serve some genuine purpose (as seen from their own perspective in the broader conflict)? If indeed it is in the best interest of the state of Israel or the Palestinian people (rather than just their respective leaderships) then it makes sense to escalate. I think the answer is no, there's nothing to be gained by escalating further.
The Israelis will not defeat all of Hamas, so escalating means there will be more violence in the future. Hamas will use any Israeli attacks to gain popularity and boost its recruitment. As anecdotally illustrated by one young recruit who was quoted by Haaretz:
Hatem, one of the teens who attended Hamas camp, is just 14, but he has already lived through three wars with Israel. Now, he’s proud of being ready for the next war. “The Israelis killed my niece last summer. Now I want to kill them,” he told the AFP news agency after finishing the camp.
From the view of the Palestinian people, it doesn't make rational sense to escalate either. Their weapons are much less advanced, so any attack will be returned multifold. This is clear from comparing Israeli vs Palestinian casualties (both in terms of deaths and wounded), for example here.
In the end, the current episode of violence is not a conflict that can be won (by either side). The best explanation, I think, is that it's politically convenient to escalate now for both sides. The political considerations on both sides are as follows:
On the one hand, there is the fragile domestic position of Israeli PM Netanyahu. According to the Washington Post on May 12th:
For Netanyahu, the escalation of fighting brought a last-minute reprieve from what could have been the end of his record run at the top of Israeli politics. Earlier this week, a group of rival political parties were reportedly within days — even hours — of forming Israel’s first government not to include Netanyahu in 12 years.
Just before tensions exploded Monday, a disparate collection of Israeli right-wing, centrist and left-wing parties, united only in their goal of ousting Netanyahu, indicated they were nearly ready to announce they had the support of a majority of parliament members, clearing the way to form a governing coalition.
By the end of the day, the political process had come to a halt. For now, amid the unrest, the prospect of a non-Netanyahu government is frozen and, political observers said, may be out of reach entirely.
“They were just about to call the president and say we have reached a deal, we have a coalition,” said Gayil Talshir, professor of political science at Hebrew University. “The riot came just in time to prevent the change of government in Israel.”
The same conclusions were reached in Israeli media. According to a compilation in the Guardian, dated May 13th:
Lapid [Yair Lapid, the Israeli opposition leader] said there had been a “complete loss of control” and accused Netanyahu of “leading us to anarchy”. He added: “Jewish and Arab rioters have declared war on Israel, and there’s no response, no government, no police, no leadership.”
Writing in Yedioth Ahronoth, Israel’s biggest-circulation newspaper, the commentator Nadav Eyal said: “We are seeing dissolution; we are seeing the fracturing of our social compact.”
Louis Fishman, an associate professor at Brooklyn College, wrote in Haaretz that Netanyahu’s “greatest magic trick” had been to blind Israeli Jews to their state’s oppression of the Palestinians. “But even the most carefully constructed house of cards eventually starts tumbling down, and that exactly is what is happening now … Impregnable Netanyahuism, the work of a master illusionist, is shattering.”
Lapid said the events of the past week were “no excuse” for keeping Netanyahu in place. “Quite the opposite. They are exactly the reason why he should be replaced as soon as possible.”
On the other hand, Hamas faces a similar situation in its internal politics. According to a Washington Post column dated May 13th:
For Hamas, its entry into the fray comes amid a tangled intra-Palestinian squabble. It’s at odds with Palestinian Authority President Mahmoud Abbas, whose Fatah faction holds nominal sway over the West Bank. (In an earlier era, Israel allowed the emergence of Islamist outfits like Hamas in a tacit bid to undermine the strength of more-secular Palestinian resistance groups like Fatah.) Abbas decided to scrap long-anticipated Palestinian elections this month, further delaying any prospect of reconciliation among the bitterly divided Palestinian leadership and intensifying public frustration with the increasingly unpopular PA.
To illustrate how Hamas can benefit from the current violence, the following paragraphs of the same WP column further illustrate how Hamas benefits politically:
One Ramallah-based pollster and former Palestinian Authority official said: “From preliminary indicators, many people in the West Bank are admiring what Hamas is doing. We don’t know their motivations, but it was effective of Hamas to confront Israel on the basis of their support for the Palestinian people of Jerusalem.”
“Hamas does not actually want something from Israel,” wrote Michael Koplow of the Israel Policy Forum. “It is seizing upon the current moment as an excuse to capitalize on a unique opportunity within Palestinian politics, and the rockets that Israelis are sheltering from are Hamas’s effort to get a leg up on Fatah.”