Time Signatures tell us "How Many of What" there are in a measure (space between the barlines, a.k.a. bar). When we look at a Time Signature, typically we see two numbers. The bottom number tells us unit of measure (quarter note, 8th note, etc.), and the top tells us how many there are in the measure.
If we look at 3/4, the number on the bottom (4) tells us the pulse or unit of measure is based on quarter notes. The top number (3) tells us how many quarter notes we have in each measure, in this case three (3). 3/4 tells us we have three (3) Quarter notes per measure and we would "count" this as | 1,2,3 | 1,2,3 | and so on. If we look at 6/8, we can conclude there are six (6) 8th notes per measure or bar. We would count this as | 1,2,3,4,5,6 |.
Variations on grouping of beats are used in Time Signatures with larger upper (count) values. For example, 5/4 can be grouped as (or have a rhythm of) 3+2 or 2+3. 11/8 can be grouped as 3+3+3+2, or 3+2+3+3, or 2+3+3+3, or 3+3+2+3, etc. The Time Signatures 6/8 and 12/8 can be felt and counted as if in two (6/8 - 2 dotted quarter notes) or in 4 (12/8 - 4 dotted quarter notes). The groupings shown in the chart below are basic and only show how many of what type of notes are in the Time Signature.
Time Signature Abbreviations: The first two lines in the chart below show the Time Signature spelled out, followed by their Abbreviation. Either Time Signature marking can be used, they are interchangeable.