We're going all ethnic with this drum beat. It's a reggae beat with an African influence. Honestly, first few times you play this beat it might sound like a mess. Stick with it until you get it smooth. First interesting thing about this drum beat is you'll notice it's in 6/8 timing. Definately not a common reggae timing, nor rock, metal, funk, whatever. Basically, each beat has a quarter note duration but there are six of them in each bar. In other words, technically there are no "&" beats.
So, why, you may ask, is the count given under the drum beat in 3/4? That's to help you identify the main beats. Notice in bar 2 that there are no drum hits on beats 2 and 3. Usually, that's where you'd hear the bass drum pounding out the downbeat. If you're used to a straight rock beat, or maybe a stomping bass drum attack for jazz then missing these beats might seem awkward. The counts given under the drum tab are to help you get the timing of this beat down. Count it through in your head as you play it if you need to.
As we mentioned the beat is 6/8 which means the count is really "1, 2, 3, 4, 5, 6". It was much easier to explain this beat by using "&" to highlight the off beats. If you find this beat a challenge at a faster tempo bring it down to about 102 BPM. That's a nice, smooth groove.