Time signatures indicate the number of beats per bar and the length of the note that carries the beat. On the stave, the time signature goes in-between the key signature and the first note of the song.
If the number on the bottom is 4, it means that there are crotchets in the bar (also called quarter-notes). If the number is 8, it means there are quavers in the bar (also called eight notes). If the number is 16, there are semi-quavers in the bar (also called sixteenth notes).
In order to fully understand time sigunatures,just remember the bottom note is the type of beat, crotchet, quaver and semiquaver. The top note is how many of those particular beats are in a bar. The first one says 3/4, which means you will have three crotchets in a bar. The last one says 12/16, which means you have twelve semiquavers in a bar.
Here is the score for "Here comes the sun". In this particular part, there are many time signatures. These time signatures include 5/8, 4/4, 2/4 and even 3/8.
In 5/8, it means there are 5 quavers in the bar. There is a dotted crotchet which is worth three quavers, followed by two quavers which means that we are in 5/8. In the 4/4 bar, there are four crotchets in a bar. In the 2/4 bar, there are two crotchets in a bar and in the 3/8 bar at the very end, there are three quavers which means that we are in 3/8.
Can you work out the time signature for the first two bars?
Time signatures are very useful because without them, we wouldn't know how many beats would be in the bar. We could write the music in 4/4 and play it, but the starts of the bars wouldn’t correspond with the start of the phrase and therefore people's breathing and phrasing would be out of time.