Boh is the biological child of Yubaba
Boh is a large baby that belongs to Yubaba and, up until meeting Chihiro (Sen) has remained within his nursery for fear of germs. He is treated as an infant by his doting mother Yubaba. Although Boh is a baby he is able to talk, and though no age is specified, he can walk on his legs and has good muscle control. He is twice the size of his mother, and is only seen wearing a one piece full bib.
During the events of the story, he is changed by his aunt Zeniba, into a small grey rat. While this must have been a tramatizing experience, to say the least, we see a great deal of character development in his personality, that demonstrates maturity.
Prior to meeting Chihiro, Boh is a selfish and spoiled child. He was used to getting all the attention, gifts, and food he wanted from Yubaba. He also developed a fear of germs, demonstrated by his initial hindrance in leaving his nursery. However, his personality quickly changes during his adventures with Chihiro. He developes a strong affiliation with Yubaba's bird, who was turned into a fly-like creature and would often fly him around. By the end of these adventures, we see him standing up to Yubaba to help Chihiro.
It is also suggested that, prior to meeting Chihiro, Boh was unable to stand or move on his own. This is seen through Yubaba's surprise at seeing Boh standing after his return with Chihiro.