A brief explanation of this very common musical term.
Common Time is a term associated with Time Signatures and in its most basic form is just another, more short hand way of referring to 4/4. In some pieces of music you may see the time signature replaced with a 'C', this means exactly the same as if 4/4 were written.
I tend to give Common Time a slightly more specific definition, particularly when it comes to drum kit parts. To me it refers to any time the piece is in the time signature of 4/4 and there is a strong emphasis on the second and fourth beats, such as in the groove shown below.
There are other forms of 'time' within 4/4 such as half, double and quarter each of which have there own slightly more specific accent placements within the bar.