Where does the expression “old hat” come from and What does old hat mean?

The expression “old hat” means: Old stuff; information, experience, condition, or the like that is familiar.

A gutter interpretation of the origin, based on the pun, “frequently felt,” does not strike me as remotely plausible.

In our opinion the familiarity that is implied is rather that of long usage, something to which one is as accustomed as he is to a hat so long worn as to fit the head snugly.

The metaphor is comparatively recent, and is rarely heard in the United States.