Mr. and Mrs. Beaver are a pair of talking animals who meet and care for Peter, Susan, and Lucy (and Edmund, to the best of their ability). They're particularly notable for their virtue and domestic peace and seem to represent all the "upright citizens" of Narnia.
Mr. Beaver is an hard worker; he built his own home in the top of his dam on the river, and he brings home the bacon...and by "bacon" we mean "freshly caught fish." Mrs. Beaver is domestically-minded; we first see her working at her sewing machine, which she worries about when they are forced to flee their home. The Beavers are fiercely loyal to Aslan and resist the tyranny of the Witch; they believe in ancient prophecies and accept that Narnia should be ruled by human beings.
It might be most useful to think of the Beavers as a Narnian version of solid middle-class middle-English citizens in the 1930's. Like the stereotypical midcentury married couple (think Leave it to Beaver – pun intended), the Beavers have a traditional division of gender roles, value hard work, and believe in the mainstream religion and government around them.
They accept that their position is subordinate to many of the grander people around them, and they're happy to serve and do their own small part. They refuse to compromise their values to increase their safety and will stand up for what they believe in no matter what. Their primary flaw is probably a lack of imagination; they don't think much can be done to redeem Edmund, and they, like many others, are surprised when Aslan has to sacrifice himself to the Witch.