What do terms like "I yield back" and "I reclaim my time" and "I yield to..." mean? I sorta get it, but am still quite clueless as to the details, let alone any name it may have.
Rules of debate are meant to help maintain order and decorum amongst people who may have wildly different opinions on matters, and to facilitate a timely and smooth legislative process.
The phrases in particular you mention are relevant to various limits on how many times, when, and for how long a person may speak, and what they are allowed to do with the time they are allotted. If they are permitted to let someone else speak during their time, they may "yield [their time] to" that other entity; if they were already speaking on someone else's time, they may "yield [the remaining time] back to [the original person]". The original speaker would then reclaim their time. In each case "yield" is essentially a synonym for "give to" or "give back".
I'll also add that in your title question, the use of "Mr. Speaker" is another one of the formalities of the rules: anyone currently speaking is required to address everything to the Speaker (who controls the debate and chooses the rules). This is meant to prevent personal attacks, which would be easy to fall into on contentious issues.
A lot of this is nicely detailed in the following Congressional Research Report from 2016, concerning how time is managed in the House.
In the United States Senate, if cloture is not invoked, Senators can speak for as long as they want. However, often cloture is invoked. If it is, then according to the Senate rules:
Thereafter no Senator shall be entitled to speak in all more than one hour on the measure, motion, or other matter pending before the Senate, or the unfinished business, the amendments thereto, and motions affecting the same, and it shall be the duty of the Presiding Officer to keep the time of each Senator who speaks. ...
After no more than thirty hours of consideration of the measure, motion, or other matter on which cloture has been invoked, the Senate shall proceed, without any further debate on any question, to vote on the final disposition thereof... The thirty hours may be increased by the adoption of a motion, decided without debate, by a threefifths affirmative vote of the Senators duly chosen and sworn, and any such time thus agreed upon shall be equally divided between and controlled by the Majority and Minority Leaders or their designees.
Notwithstanding other provisions of this rule, a Senator may yield all or part of his one hour to the majority or minority floor managers of the measure, motion, or matter or to the Majority or Minority Leader, but each Senator specified shall not have more than two hours so yielded to him and may in turn yield such time to other Senators.
Notwithstanding any other provision of this rule, any Senator who has not used or yielded at least ten minutes, is, if he seeks recognition, guaranteed up to ten minutes, inclusive, to speak only.
So, pretty much, every Senator gets an hour of debate (although this is to a maximum of 30 hours unless they extend the time.) If you don't want to use your hour, or only want to use part of it, you can yield some or all your time to your majority or minority leader, and they can then in turn yield that time to another Senator, who can then use that time to exceed their hour.
Your question includes the phrase "Mr. Speaker". I don't believe that would be used in the Senate - instead, that would be used in the House. The House rules have the same concept of yielding time, but the rules are somewhat different.
When an MP is giving a speech in parliament, another MP can stand up to ask a question or give information. The speaking MP can accept or decline to take the question. If he wishes to accept the question he addresses the Speaker of the house to say that he yields his take to x MP's question. Since it his time to speak he can choose whether to allow anyone else to speak during that bit of time, in exactly the same way if he wishes to stop the question MP from talking he can "reclaim" his time.