Also known as an absolute majority. A term used in any situation of comparisons of one or more groups of things. Most commonly used in parliamentary elections and that's the situation I'll talk about.
A simply majority is when one grouping has the most votes. If we look at the results of the UK General Election 2005, they were as follows.
Clearly here, Labour is the majority party. However, when this is translated into seats (of which there are 645), due to the first past the post electoral system we have, the results were as follows.
- Labour - 356 - 55.2%
- Conservative - 197 - 30.5%
- Liberal Democrat - 62 - 9.6%
- Others - 30 - 4.7%
We can see here that Labour have over 50% of the seats. This is an overall majority - they have more seats than all the other parties put together. This means that (in theory, assuming not too many MPs rebel against the government line), they can get any legislation passed. Of course, this only applies in a 3 (or more) party system. If the election is between 2 parties (such as the US Presidential Elections effectively are) then a majority is always an overall majority.
I'm not going to get into an in depth argument of proportional representation vs first past the post and whether it's fair that the popular vote percentages were so off the seat percentages. However, one thing this system almost always ensures is a strong government that can get things done, whereas PR systems always end up with coalitions, meaning that it's harder for things to happen, and often with small parties holding the balance of power and effectively blackmailing the larger parties to get their own way. See Knesset.