Since the Goddess Eostre was so important at springtime, there was a month-long festival dedicated to her. The festival started on the vernal equinox in March and lasted throughout the majority of April. When Christianity spread to Anglo-Saxons, many of the traditions during the festival of Eostre were adapted into the ceremonies in honor of the Resurrection of Christ because they both occurred in the same month and encouraged many pagans to convert. As a result, the English name of the Easter holiday is derived from Eostre.
Now, rabbits (or hares) come into this story because they're the symbol of Eostre, but also because the rabbit has a strong connection to the moon in pagan tradition. The hare was believed to be a symbol of the moon, and the cycles of the moon are actually what determine what day we celebrate Easter each year. Easter is celebrated on the next Sunday after the Paschal moon which is the first full moon after the Vernal Equinox.