Answer: One can conclude that, if mice and humans have similar genomes, they must have a close ancestor in their phylogenetic tree. Actually, the genome between mice and humans are so similar that only few genes are found in just one of the two at a time.
Being so similar, it is very easy to understand why are mice used for human medical research, since the use of human beings is a practice considered unethical. With a very similar genome, it's possible to see how medication affects the DNA and how can a disease be fought properly. This way, mice in research are considered to be the human test.