Bubonic plague is a disease spreads through infected fleas. Plague-infected rats carried plague-infected fleas, the fleas bit humans. Hence rats get the blame as the vector. There are, to be sure, other potential mammalian vectors — but rats have traditionally been one of the "reservoirs" of plague fleas.

It is of note that epidemiologists are not completely sure of the "Black Death" was bubonic plague, or only bubonic plague. There are some who have argued that the symptoms and spreading also appear to have included pneumonic plague, that is spread through spit and droplets in the air, which is a very different sort of vector.

One very nice overview of the plague and its impacts is William H. McNeill's Plagues and People, though it should not be considered the last word on exactly what type of plague the "Black Death" was (which is as I understand it still not totally certain).