| 4/4, 6/8, and other terms like that are used to detemine one characteristic called meter. Basically, it will determine the feel of a particular piece of music. There are three different types of meters: Simple, Compound and Odd Meters. Oftentimes, Compound anf odd meters are combinations of simple meters.
Anyway, if you check some sheet music, you'll usually see the numbers you refer to in the beginning of the first measure of the piece. The bottom number indicates which note unit gets the beat, while the top number indicates the number of beats per measure. For instance: 2/4 meter indicates that there are two beats per measure and the quarter note equals one beat. Sousa marches and band music in general is in 2/4. 3/4 is waltz time three beats per measure, quarter note = 1 beat. 4/4 is also called '"common time" and is sometimes indicated not by two numbers, but simply by a "C" where the meter indication should be. Most popular music that you hear today is in common time, hence the name.
Compound meter is basically the same as simple meter, but can also have different accents and is more "shuffle-ish" for want of a better term. to obtain compound time signatures all one has to do is mustiply simple meter time signatures by 3/2, therefore, 2/4 becomes 6/8; 3/4 becomes 9/8 and common time becomes 12/8. A lot of blues and ballads are in compound meter.
To feel the differences, you could set a metronome in "two" and then count on each beat -
"ONE, TWO,ONE, TWO", etc for 2/4
whereas, 6/8 would be
"ONE, two, three; TWO, two three", etc. over the same tempo as above. Check out "Norwegian wood" by the Beatles. It's in 12/8, but you'll get the drift.
Finally, Odd-Meter is any time signature that doesn't fit into either category mentioned above. The best known odd-meter tune is Paul Desmond's "Take Five", on Dave Brubeck's Time Out album. as the title suggests, the meter on the tune is 5/4. This time sig is still pretty simple, as it can be briken down into one measure of 2/4 followed by one of 3/4 or vice versa, but there are musical genres that subdivide music in ways mych more complex than the west - India comes to mind.
King Crimson has also performed a lot of odd-meter tunes. Bill Bruford said in an interview that Crimson was the only band who could play tunes in 11/16 (11 notes per measure, beat unit = 16th note = one fourth of a quarter note).
Hope I didn't make it more complicated. I highly recommend lessons. You'll enjoy music more.
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