Question: I've encountered the notation $|G|$ (for a finite group $G$) but I haven't seen it before and the text didn't define it. What does it mean?

If it's relevant, it appeared in the context of defining this, for $f:G\to \mathbb C$ continuous:

$$J(f) = \frac{1}{|G|}\sum\_{g \in G}f(g) $$ 

From the looks of it I would guess $|G|$ is some sort of "size" of the group. Perhaps it's the number of elements of $G$?

Answer: 
Posting so you can mark this as answered:

The notation $|S|$ denotes the carnality of any set, and is frequently used with groups and rings as well. It's less useful for fields, as finite fields are usually indexed with their cardinality, but it will show up there from time to time as well.
"Cardinality" or "Order"

Simply the size of the set.

If G= {2,5,6,8}

|G|=4