On[symbol::tag] switches on a message, so that it can be printed.
On[s] switches on tracing for the symbol s.
On[, , ... ] switches on several messages.
On[ ] switches on tracing for all symbols.
When tracing is switched on, each evaluation of a symbol, on its own, or as a function, is printed, together with the result.
Note that the tracing information is printed when a function returns. As a result, traces of recursive functions appear in the opposite order from their calls.
On[s] is equivalent to On[s::trace].
On[ ] is equivalent to On[s::trace] for all symbols.
See The Mathematica Book: Section 1.3.11 and Section 2.8.21.
See also: Off, TracePrint.