That's a bud trying to become a branch.
Figs form at the leaf nodes. For main crop figs, look at the spot where the stem of a leaf meets the branch. it'll look like a little BB.
Re brebas (you'e in the same zone as me), you'd see buds in April/early May on potted plants at former (last year's) leaf nodes. By now they would either (a) have dropped, because many varieties don't like to ripen brebas; or (b) have grown so that they'd look little figs, maybe the size of a dime to the size of a quarter.