1. Naturally collects Armor/AP which frees up spots in his inventory 2. He has a soft-pull/engage tool 3. His lantern lets them preform big plays and back out really quickly, also provides a nice shield. 4. Push/pull enemies for engage or escape 5. Ultimate is really nice in teamfights or ganks.
Leona is a balls-deep kill-lane support. You need a decent amount of communication with your ADC or at least someone that knows when to go in and keeps an eye on you. You're tanky as hell early on and all of your abilities have you sticking close to the enemy and stun locking a priority target. With a bursty ADC like Graves or Draven, you can easily kill someone from full hp once you hit level 2 or 3.
So basically, get your skills, ping the adc, pop your W when you see a good chance to land your E, let your adc proc the passive from E, Q stun them, W explodes, exhaust if they're not dead yet.