When you are in the groove, everything just feels right. The “pocket” is deep, and all the music parts are moving together to create a beautiful sound. This goes for any style of music. When the groove is good, all is good.
Breathing is just as important for drummers as it is for singers. Drummers have a more physical job than some other instrumentalists, so it really helps to have good breathing habits when you play. For instance, have you ever checked to see what your breathing is doing when you play a complicated drum fill? Do you hold your breath or let it flow? Do you tense up or stay relaxed? Staying relaxed and breathing help tremendously to keep good time especially during drum fills. Many amateur and beginning players have a strong tendency to slow down or speed up during fills, which can really make a song sound clunky and disjointed. I highly suggest that when you practice, set aside some time for breathing exercises while you play. 
The first thing to try is to get your trusty metronome and set it to a medium tempo of about 108. (You have one of those, right? If not, then you most definitely should; here are some great suggestions: the BOSS DB-30, DB-60, DB-90; the Tama RW200 Rhythm Watch; or the compact Tama RW30 Rhythm Watch Mini.) Play a simple beat and inhale short breaths for four beats and then exhale short breaths for four beats. After you get a rhythm going for that and feel comfortable, start adding in one-bar drum fills while still doing the same breathing exercise. Eventually, move on to two-bar, three-bar, and four-bar fills, all while keeping your breathing steady. Another thing to try is to inhale and exhale in long breaths — in for four beats and then out for four beats. Again, after you are comfortable, start adding in your drum fills. The final thing to do is to breathe that same exact way at your gigs. If you practice this enough, it will become second nature, and you won’t even think about it.