From baba ("father") + tún dé ("come again"): "father has returned." Traditionally given to a boy born after the death of his father or grandfather, understood as that man's return to the family. Shortened to Tunde.
Source: Yoruba (Nigeria) name; meaning ("Father has returned"), breakdown (baba-tún-dé) and usage from yorubaname.com, entry "Babátúndé". Wikipedia's "Babatunde" article gives the same meaning and lists Tunde among its variant forms.