Not quite sure what it is, but it isn't Crassula ovata. Very different stem, leaves and growth habit. I think those are branches - or possibly inflorescence??? - and do not need to be pruned off (unlike suckers on a tomato plant :))

Here's another picture. Maybe this will help ID the succulent?

Good photo - hope someone knows; I can't figure it out!!!

Just for comparison, here is Crassula ovata:

sedum praealtum