Can anyone explain to me how this mechanic works?

I am just wondering if it gives you health based on
your attacks to enemies or their attacks upon you?

ie. "absorbs 6% of lightning damage"

^ iirc, it gives you back %life after you've taken the hit - e.g. you're hit for 100 with a fire spell and you have 12% fire absorption, you'll get 12 life back right after the hit, assuming you've survided.

Yeah it heals you after you take damage from that type.