Off[symbol::tag] switches off a message, so that it is no longer printed.
Off[s] switches off tracing messages associated with the symbol s.
Off[, , ... ] switches off several messages.
Off[ ] switches off all tracing messages.
The value of symbol::tag is not affected by Off.
Off[s] is equivalent to Off[s::trace].
Off[ ] is equivalent to Off[s::trace] for all symbols.
See The Mathematica Book: Section 1.3.11 and Section 2.8.21.
See also: On, Message, Check.