--> is the relation that the judgement rules are defining. It's usually pronounced "steps to" or "reduces to". You can think of this relation as the analogue of "showing your work" in algebra:
(1 + 2) * 3 --> 3 * 3 --> 9
It's used as a way of specifying the semantics of a programming language through a binary relation on programs. These kinds of semantics are called small-step semantics. Within small-step semantics, there are approaches include reduction semantics and structural operational semantics. If the program is augmented first to a "configuration" that includes extra components like environments and stores, and the relation is on these configurations instead of just plain program terms, then it's called an abstract machine semantics.
Note: Sometimes you define multiple relations and build up more complicated relations out of them, so you have different arrows.
There are other kinds of operational semantics (eg big-step semantics) and there are other kinds of semantics besides operational semantics.