When something gets hurt a number pops off it showing how much health it lost, along with what did it. Healing shows up too. The numbers bounce once or twice and fade away.

These are in the assorteddamagenumbers-client config file. They only change your own game, so everyone can set their own.
damageNumbers.showSource shows what did the damage beside the number. On by default.damageNumbers.showHealing shows healing as well as damage. On by default.damageNumbers.range is how far away numbers still show. 24 blocks by default.damageNumbers.lifetime is how long a number stays in ticks. 40 by default, which is 2 seconds.Damage Numbers also comes in Assorted Util with the other five Util mods, if you'd rather have them all in one download.
The full guide is at assortedmods.com. It's also in the game, in the Instruction Manual from Assorted Lib.
Found a bug? Report it on GitHub.