Mice are not, as is commonly assumed on planet Earth, small white squeaking animals who spend a lot of time being experimented on. In fact, they are the protrusions into Dimension Q of hyper-intellegent pan-dimensional beings. These beings are responsible for the creation of the Earth, having commissioned it from the Magratheans to calculate the Ultimate Question of Life, the Universe, and Everything. The whole business with the cheese and the squeaking is just a front.
Two mice, Frankie and Benjy, escaped from Earth before the premature termination of its program by a Vogon Constructor Fleet. They had belonged to an Earthling known as Trillian. They were rather keen to remove Arthur Dent's brain to reveal the ultimate question, which they had devoted a lot and time and money to finding.