？
Would you like something to drink?
Literal
Something honorific-drink-become [polite-question-ますか]?
A textbook example of sonkeigo (honorific speech). The pattern お + verb-stem + になる elevates the listener's action: 飲む → お飲みになる ('you honorably drink'). This is the go-to pattern for raising the status of what your customer, guest, or superior is doing. Compare the humble equivalent for your own actions: お + stem + する.