Triggers connect your drums to a drum module so that you can "trigger" the electronic sounds.
For recording, the advantage of triggers is that you can get a "bigger" more even sound from the drums without needing several mics, and channels on the board, etc. etc. (although some people get a great drum sound with only 2 or 3 well placed mics).
The disadvantage is that nothing sounds better than a well tuned well miced kit. Even the best e-drums fall short of a well tuned kit (I've got v-drums - and I still prefer to record real drums - if I have the right room, etc.)
Also, keep in mind that even if you trigger the drums, you will be using the live cymbals, so you still need a mic(s) to record the cymbals.
If you plan to use triggers in a gigging situation, you also need to consider the need for a PA that can take the low end abuse - and you also need onstage monitors, etc.
As you can see, getting triggers is only a start - by the time you get a module and the triggers, you would spend about the same as buying 4 SM57's.