For this discussion, I'm going to assume there are only integral votes; That is, it's not possible to cast half a vote. There are certain kinds of votes where fractions are allowed, and the rules are not the same there.
A "majority" = "more than half." It does not mean "50% plus 1," although many people casually toss this out because it fits the easy case of 100 votes cast. In that case, 50 votes is not more than half, but 51 votes is. But what if there were 101 votes cast? In that case, 50% of 101 is 50.5, and if you add 1 to that, you get 51.5, and 51 is less than 51.5.
Another common but wrong statement is that a majority is 51% of the votes cast. Assume 1000 votes cast: if you (foolishly) defined your majority as 51%, then a vote of 509-491 loses, because you needed 510 votes to pass. (I'm assuming the simple yes-no case, but you can construct similar cases in multi-way elections.)
More generally, a majority is the first integer that is more than 50% of the number of votes with a preference cast in the election. In Excel, the formula is =ROUNDUP(([X]+1)/2,0), where [X] is the total votes cast. Thus 100 votes = (100+1)/2 = 50.5, rounded up to the next highest integer = 51 and 101 votes = (101+1)/2 = 51, which doesn't need rounding because it's already an integer. [Corrected formula and narrative after commenter pointed out mistake.]
Unless specifically qualified, "majority" means "more than half." There are other kinds of majorities, such as a "two-third majority." The phrase "simple majority" is redundant, but I guess necessary for people who assume that "majority" doesn't have an unqualified meaning.
Speaking of a two-thirds majority, note that it doesn't mean 66%, 67%, or 66.7%, but the first integer number that is at least, but not necessarily more than, two thirds of the total votes cast with preference. The easiest way to calculate it on the fly in a yes/no election (assuming the case where you need two-thirds to pass) is to double the number of no votes. (=IF([YES]>=[NO]*2,"MOTION CARRIES","MOTION FAILS") in Excel and other spreadsheets.) Note that exactly two thirds is okay, unlike a majority, where exactly 50% does not win.
Blank ballots, abstentions, and explicit votes for "No Preference" (like on site selection ballots) do not count as votes cast. If there were 100 ballots cast, with 99 blanks and 1 yes, then the vote passes 1-0. One reason I never call for abstentions is that someone who says nothing when you ask for abstentions has abstained just as much as someone who shouts out when the call is made. Abstentions are not votes; they are the lack of votes. The only reason you should ever have a need to even record them is if there is ever a need to confirm that a quorum was present.
In WSFS and Westercon rules, when you reach "No Preference," your ballot is now removed completely from the count regardless of whether or not you had lower preferences. That is, "No Preference," being equivalent to a blank ballot, is an abstention. Sometimes we say that No Preference is "sticky."
"None of the Above"/"No Award" (site selection/awards balloting) is not "sticky." It is a candidate like any other and is treated like any other candidate. (Aside from some special WSFS rules designed to make No Award/NOTA more likely to win, but that in practice are unlikely to ever apply, that is.) This means that in a preferential ballot, if you have preferences after No Award/None of the Above, you should rank them. Approach the remaining candidates as "I really don't want any of these candidates to win, but if one of them must win, I prefer [X]."
You can of course adopt your own special rules that give special definitions for how many votes it takes to pass something or for someone to be elected, but the figures here are the defaults in general parliamentary law, and when you use any of the words in an unqualified way, this is what you should be expecting.