It really depends on whom you ask. Depending on the context, people talking about "Palestine" could be referring to a few different things, though some definitions are more controversial than others. Barring historical definitions, like British Mandatory Palestine, Palestine could mean any of the following, in reverse order of controversy:
The least controversial definition of Palestine would refer to Areas A and B of the West Bank, as well as the Gaza Strip.
(Note that this image does not show the Gaza Strip.)
The Oslo Accords divided the West Bank and the Gaza Strip into three sections, areas A, B, and C. Area C is under full Israeli control, Area B is under Israeli military control but Palestinian civil control, and area A (comprising major Palestinian population centers) is under Palestinian military and civil control. An interim government, the Palestinian National Authority, was set up to manage Areas A and B until a final settlement could be reached. However, after Israel ceded all areas of the Gaza strip to the Palestinians in 2005, Hamas violently overthrew the Palestinian Authority government in Gaza and established control over Gaza.
This means that different governments control the Gaza Strip and Palestinian areas of the West Bank, but as these areas are under Palestinian control, and as Israel granted the Palestinians these areas, there is little controversy as to whether or not these areas should be under Palestinian control. All parties in the conflict recognize Palestinian control of those areas (though the PNA and Israel object to Hamas' control of Gaza), so we can, without much ambiguity, refer to Areas A and B of the West Bank, as well as the Gaza Strip, as Palestine.
However, Palestine is often used to refer to all of the West Bank and Gaza within the 1949 Armistice Lines.
This would include area C (though the term more traditionally used for these areas, albeit still controversially, is "Palestinian Territories"). Here you will find much more controversy, as many classify area C of the West Bank as part of Israel, or at least not as Palestinian.
The 1949 Armistice Lines (often called the 1967 borders, or the Green Line) were created after Israel's war for Independence in agreements with the surrounding Arab states. Egypt had captured the Gaza Strip, and Jordan had captured the West Bank. The armistice lines defined temporary borders (the agreements stressed that the borders were temporary and only existed out of military necessity), and acted as borders until 1967. In 1967, Egypt blockaded the Straits of Tiran, which Israel had said it would consider an act of war. In response, Israel destroyed the Egyptian air force. Egypt, Syria, and Jordan attacked Israel, but Israel repelled the attack and defeated the Arab forces in six days.
Israel captured the West Bank, Gaza, and the Golan Heights (which are not usually considered part of Palestine). These areas are usually defined in terms of the armistice lines. Areas captured from Jordan comprise the West Bank and areas captured from Egypt comprise the Gaza Strip.
Israel's possession and sovereignty over territories beyond the Green Line are not internationally recognized, even in the case of Area C, which parties agreed in the Oslo Accords would be under Israeli control until a final settlement had been negotiated. Many countries and governments, including the Palestinian Authority, believe that all of the West Bank should belong to the Palestinians. As such, the West Bank and Gaza are often referred to as Palestine, or Palestinian Territories (or Occupied Palestine, or the Occupied Palestinian territories, etc).
However, such definitions are controversial. Israel is currently in control of Area C of the West Bank, as per the Oslo Accords negotiated between Israel and Palestine, and feels that Area C belongs to it until it should choose to withdraw from Area C as the result of a final settlement. If you want to refer to the West Bank and Gaza, it is probably best to just refer to them as the West Bank and Gaza, as these terms do not imply any rightful owner.
Finally, Palestine is occasionally used to refer to all land West of the Jordan River.
This would include Israel, the West Bank, and Gaza. Such usage is frowned upon, as it fails to recognize Israel's sovereignty within the parameters of the 1949 Armistice Lines. With the exception of most Muslim countries, North Korea, and Cuba, most countries recognize Israel's right to exist. This means that use of the term "Palestine" to refer to land including Israel is often used by extremists, like Nasrallah (leader of Hezbollah), who believe that Israel should not exist.
So, the meaning of "Palestine" isn't well-defined, but can be used to refer to areas under the control of Hamas or the PNA (without much ambiguity or controversy), can be used to refer to the West Bank and Gaza (which is not uncommon, though is definitely controversial), and can be used to refer to all land west of the Jordan River (which is an extreme and, to the degree that the existence and legitimacy of countries is an objective matter, incorrect usage of the term).
