In Judaism, what does it mean to wrestle with a divine being?
This is a great question. Undoubtedly, this is referring to the only place in the whole Bible where a person wrestles with God. This episode occurs in Genesis 32 where one of the patriarchs, Jacob, wrestled with a divine being all night long before he is about to his brother (Esau), whom he has cheated out of a birth right.
Jacob holds onto God all night and does not let go. In fact, Jacob holds on for dear life and asks for a blessing. The divine being blesses him, but in the process Jacob is given a limp. After this bout with God, Jacob is given a new name, Israel.
As for the meaning of this passage, I think two points are communicated. First, it is important for Jacob to realize that he cannot get away with anything he wants. Thus far in Genesis he has been incredibly deceptive. He stole his brother's birth right and stole his father-in-laws animals. Now he faces God and he knows that he cannot win or get way. Second, it shows that we need to pray and wrestle with God in prayer. This is how most commentators take the passage.