“Compute” is a term that is used in a variety of contexts, but in discussions of serverless services such as serverless functions or databases, “compute” is typically used as shorthand for the computing resources (such as CPU, RAM, GPU, etc.) required to perform some kind of action.
In the context of a serverless database such as CockroachDB Serverless, for example, the amount of “compute” – i.e. computing resources – your database uses each month processing queries is one of the factors on which billing is based.