Subdivision is the idea of splitting a larger phrase of music into smaller sections.
Generally speaking, when you subdivide something you split it into smaller parts. For example, when cutting a cake each slice could be thought of as a subdivision of the whole cake. This idea can be applied to rhythms within music and you will probably have seen it used many time without even realizing it.
The most simple example of this can be seen in this lesson on the Single Stroke Roll. On that page there are three different rhythms used, one made of crotchets, one made of quavers and one made of semi quavers. Each of these can be thought of as both a subdivision of the bar but also as a subdivision of the previous exercises.
In the time signature of 4/4, you have four beats worth of music. Playing four crotchets within that space means you have 'subdivided' the bar into four equal parts. Likewise, if you played eight quavers you would have created eight equal subdivisions and with semi quavers 16 equal subdivisions.
This can also be applied to individual beats of music, technically giving you multiple layers of subdivision. Let's say you're counting quarter notes on the bass drum. If you were to play eighth notes on the snare on top of that, the snare would create two equal subdivisions of the kick. If you were to play semi quavers over the same kick pattern you would have four equal subdivisions. Playing eighth note triplets over that same bass drum pattern would create three equal subdivisions.
This idea can be used to great affect if some thought is put into it. Some very cool tricks can be made around the idea of syncopation and creating new groupings within that. The intention of this lesson though is to give you a basic understanding of what subdivision is and how it is used within drumming.
Just to drive the point home a little more let's look at a couple of diagrams. This box represents a bar of music:
If we put two more boxes inside that box we have subdivided it into two parts. So to put that in musical terms, we still have the big box that represents the bar then inside that we have two boxes that represent two even notes within the bar, which would be minims.
By the same logic, if you were to split that up into four boxes then each box would represent a beat of the bar. Or in musical terms, each smaller box represents a crotchet within the bar.
Splitting a bar into quavers could be represented like this:
See if you can create diagrams for how various triplets would fit into the bar.