there's 2 things that make a champion a good support:
1: synergizes with the adc well in lane
There's many ways that you can be good in lane. healing the adc/shielding them, poking away at the enemies, getting your adc fed(agressive supports like leona/blitz). Pretty much anything that will help your ad carry get more cs than the enemy or kills, and bring them ahead.

2:useful in late game with minimal farm
You can't have someone like katarina as a support, because she will do little to nothing late game without her farm. You need people with utility like stuns, thresh's lantern/pull, and all kinds of stuff. Even without lots of damage items or tankiness, these characters will still provide a huge influence in a teamfight.

Support annie fulfills this role because she has good laning with her burst damage and stuns allowing the adc to get fed, and can poke with her very high range.

She transitions into late game well with low farm because she has the ability to stun multiple targets multiple times within a teamfight, so she influences them a lot.