The term "musical form" refers to the structure of a song or piece of music, e.g. verse, verse, chorus, verse, or 12 bar Blues. Most songs you play in a band situation fall into two categories. One is the 12 bar Blues form which you have already learnt and the other is songs which break down into 8 or 16 bar sections.
When you are playing a song, it is important to think about the length of sections or verses as this largely determines the way all of the musicians will play. Listen to some of your favourite songs and notice the way the drum part changes, e.g. fills, crash cymbal etc at the end and beginning of verses. Listen also to dynamics and interplay between the parts. A great way to practice getting control of the form of a song is to sing the lyrics as you play your part. In fact, singing either the lyrics or the bass line is great for your coordination and independence as well as making you much more aware of what your drum part is ultimately fitting in with and complementing. Another useful exercise is to actually count the bar numbers as you play. E.g if you are playing a song in * time, instead of counting 1 2 3 4, 1 2 3 4, you could count 1 2 3 4, 2 2 3 4, 3 2 3 4, 4 2 3 4 etc. After a while you begin to know instinctively where you are in the song. Written below are typical examples of an 8 bar form and a 12 bar Blues form. Each one has chord symbols written above it just as you would find on a song chart.