When doing a wide grip bench you are activating your lats, chest, and shoulders more than you would in a close grip bench because those muscle become more involved in stabilizing the weight. On a closer grip bench you triceps are under tension throughout the whole movement because they are the primary pusher in that situation, but with the wide grip you getting push from your other three muscles and then the triceps kick in up top for the lockout. If you want more tricep activation on a wider grip bench press then make sure to try and rip the bar apart with your hands throughout the movement, as this will put a lot of tension on your tri's. Conversely if you want more chest activation you would try to squeeze your hands together as you press. Finally if you are not using proper technique when benching you should not take a wide grip, but if you are doing everything with good form wide grips are a great and safe way to bring up your chest. Here is a little checklist of what you should be doing when benching:
1: Arch yourself so that you are set up on your traps, and your butt is on the bench.
2: Set your feet on the ground, and try to drive yourself through your heels and back onto your traps more
3: Pull your shoulder blades back and try to pinch the bench with them throughout the whole movement
4: Tuck your elbows as you come down and try to touch the bar to your upper abs
5: Keep your lats tight throughout the whole lift
6: Push your stomach up to the bar as you bring it down, if your butt starts to come up you have to set your feet out wider
7: Squeeze the bar hard and keep your wrists up throughout the movement
8: Do face pulls after ...