Majority means the greater number of something. The opposite is minority.
If more than half the people are right-handed we can say that the majority of people are right-handed. A minority of people are left-handed. In fact, nearly everyone is right-handed, so we can say that the "vast majority" are right-handed, and only a "small minority" are left-handed.
If a political party gets a majority of votes, it means that they get more than any of the other parties. Example: if there are three parties, the winning party may have a majority of 40% while the other two each have 30%. An "absolute majority" means more votes than all the other parties together, i.e. more than half the total votes.