Aside from the duration of notes, how many beats in a measure, and what note gets a single beat. A time signature indicated the feel of the music. This is what distinguishes time signatures like 2/2 and 4/4. If you were to just look at it as how many beats a measure and what note gets a beat, you could say a piece of music written in 4/4 could also be written in 2/2 as well. Alittle translation of notes and this could easily be done and then confused, if you don't understand the true logic behind time signatures. The difference between 2/2 and 4/4 is the feel and flow of the beats. Drummers will be more familiar as calling them either upbeats or downbeats. This is still important to any other musician cause it gives the music flow. Now look at how 2/2 and 4/4 are different in this manner.

2/2 consists of a strong upbeat then a weaker upbeat. Sort of like this if you were to count it.

2/2 - 1(accented upbeat) 2 (regular upbeat)

Now 4/4 is the same as 2/2 in starting with an accented upbeat and then a regular downbeat, but it contains 2 downbeats which are in between the 2 upbeats. Sort of like this.

4/4 - 1(accented upbeat) 2 (downbeat) 3 (regular upbeat) 4 (downbeat)

Now you may see 2/4 and think how it fits with this pattern. Well it's an accented upbeat, then a downbeat. 3/4 is probably the most recognizable with this logic, because it is the waltz signature. Now if you've ever seen people being shown the waltz, they're always counting it, 1, 2, 3. And 1 is always accented, apply that to the above signatures.

Hopefully that makes sense. To a beginning musician this probably seems practically useless, but it is very powerful knowledge when it comes to writting and understanding music. Very Powerful.