What does 10 Vols mean?
I think you mean "wash resin 3 times with 10 vols of the extract buffer".

Vol means volume strength. It tells you how much of a certain element in milliliters will be RELEASED from a certain substance. In this case, your buffer is supposed to release 10 vol of something. That's all it means.

However, I am surprised about the usage of vol in this context. Volume strength is usually a term directly associated with hydrogen peroxide, and dealing with the release of a certain volume of oxygen.