In fact, they are the protrusions into our dimension of hyper-intellegent pan-dimensional beings. These beings are in fact responsible for the creation of the Earth.

Two mice (Frankie and Benjy) escaped from Earth before the premature termination of its programme. 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.

The whole business with the cheese and the squeaking is just a front.