In Short
A Bombe is an electro-mechanical machine invented by Alan Turing and
Gordon Welchman. It consisted of several Enigma machines, and was used
during the second world war, in the allied attempt at figuring out the daily
enigma settings in use by the Germans. This system was installed at bletchley park.
To be able to work, the bombe would have to have a Crib. This is a guessed
plain-text message, for example "Uber".
The german weather stations, in particular, would use specific words in
the begin of their messages (such as "hello, this is the weather station
in Narvik"). This was then put into the Bombe, and the machine would
continue trying combinations until that phrase (or part of it) was found.
What it did
The goal of the original bombe was to figure out what sockets in the Enigma
were connected to what other sockets, and also what the wheel order of any
particular day was (i.e which of the five wheels went in which of the three
slots)
The bombe couldn't do this. Instead, it tried to figure out which connections
it couldn't possibly be, leaving as few as possible to try out by hand.