Eosturmonath [April] [is] called after a goddess of theirs named Eostre, in whose honor feasts [festa] were celebrated in that month.
This lone sentence from chapter 15 of Bede of Jarrow's De Temporum Ratione ("On the Reckoning of Time"), along with the fact that, from very early times, a Christian festival came to be called by her name, is literally all that we know about the Anglo-Saxon goddess Easter. Literally all.
Under the circumstances, scholars have tended in two directions. The Maximalists have viewed Easter as a pan-Germanic goddess, herself a reflex of a pan-Indo-European Dawn goddess whose sister-selves include Vedic Ushas, Greek Eos, and Latin Aurora.
The Minimalists—many of them clearly driven by pique that so Christian a festival should bear so blatantly pagan a name—deny that such a goddess ever existed at all, and seek alternate (and non-pagan) derivations for the name of the church's great spring festival.
In Pagan Goddesses in the Early Germanic World: Eostre, Hreda, and the Cult of Matrons, Philip A. Shaw, lecturer in English and Old English at Leicester University, in a work surprisingly readable for all its dense erudition, attempts to stake out a centrist ground midway between maximalist and minimalist positions. Of greatest interest to the contemporary pagan reader (to this contemporary pagan reader, at any rate) is his marshaling of new information to shed new light on the subject.