Mother Rabbit is a widow, looking after a rather large family of young children (including Skippy, Sis and Tagalong).  She is one among many of the common folk of Nottingham.  She is a sweet but occasionally (and mildly) stern mother who prefers to impart traditional values upon her children, including good manners.  And she loves them all very much.  She also has a great love and respect for both Robin Hood and Maid Marian, both of whom do their best to look after and protect the citizens of Nottingham.

When she throws a birthday party for her oldest son, Skippy, the Sheriff of Nottingham suddenly barges in through their front door and, using his cheerful guile, convinces Skippy to open his present while he's watching.  When Skippy does this, and learns that his present is a farthing*, the Sheriff steals it from him, which leaves the boy in tears.  Mother Rabbit reprimands the Sheriff, noting that the while family scrimped and saved to give the farthing to him.  The Sheriff feigns sympathy for them, and then gives them empty encouragement.  But then Robin Hood, initially in disguise as an old, blind beggar (in order to fool the Sheriff), appears and saves Skippy's birthday by bringing presents to him, cheering he and his family up immeasurably.

Origins of the character: While there are no specific foundations for this character in the Robin Hood legends, Mother Rabbit does represent a sample of the average citizens of the village of Nottingham.

*It's worth noting that, in historical terms, the farthing coin was not first minted until after the deaths of King Richard and Prince (later King) John.  At least in historical terms.  Not terribly important from a movie perspective.