Counting triplets is tricky in the beginning, but once you figure it out, it has a very nice feel to it.
Triplets are basically "three in the space of two". So when you're looking at 16ths versus 16th triplets, three triplets occur in the same time as two regular 16ths. This is consistent with what the others have said, but also applies to any type of triplet. Eighth note triplets are three notes in the same amount of time that two regular eighth notes would be played.
The name "triplet" eluded me too in the beginning since I also thought it just "had to" mean three in the space of one. Try tapping your knee while sitting down. With left hand, tap/count 1,2,3,4 very slowly, with the right count 1,2,3, 2,2,3 3,2,3, 4,2,3 in the same timeframe. If the left is counting quarter notes, the right is counting 8th triplets. Here you can see that with the left hand, four notes are played in a "bar" and with the right 12 notes are played in that same bar. If you can do this with your hands, you can play the drums too (just kidding)
but you might hear the triplets on the ride cymbal sometimes while the kick and snare are falling on one and three recspectively.