Wordorigins.org

The original sense of the phrase up to snuff is knowing, sharp, not easily deceived. It dates to at least 1811 when it appears in John Poole’s Hamlet Travestie, a parody of the Shakespeare play:

He knows well enough The game we’re after: Zooks, he’s up to snuff.

By the early 20th century, the phrase had acquired the current meaning of meeting the expected standard. From a 4 November 1931 article in the magazine Punch:

Now Romney painted well enough, And Reynolds too, they say, And Gainsborough’s things are up to snuff, And Lawrence had his day.

The snuff is a reference to the form of tobacco. Presumably, someone who is up to snuff is adult and worldly. Literally, it is one who knows how dangerous snuff can be.

(Source: Oxford English Dictionary, 2nd Edition)