Originally, a day out where one would sign up for a
trip headed to an
unknown destination.
The Beatles'
Magical Mystery Tour film gives a little idea of what this was like (normally minus the
surrealism and
rock music, of course).
The Book of Heroic Failures records an
English couple who were on holiday in
Wales, took a mystery tour bus starting in Wales, and ended up back in their own English hometown unexpectedly.
Now, often used for poking around an unfamiliar web site or just following links randomly.