The pomegranate denotes immortality, multiplicity, unity, perenial fertility, fecundity, plenty.
In Buddhist culture it is one of the the three blessed fruits, the others being citrus and peach.
In Chinese culture it represents abundance, fertility , posterity, numerous and virtuous offspring, a happy future.
Christian: Eternal life, spiritual fecundity, the church, the seeds being the numerous members.
Graeco-Roman: Spring, rejuvenation, immortality, fertility, the emblem of Hera/Juno and of Ceres and Persephone as the periodic return of Spring and fertility to the earth. It is also the plant which grew from the blood of Dionysos.
Hebrew: Regeneration, fertility. The pomegranates with the bells on the priestly vestments represent fecundating thunder and lightning.
From "An Illustrated Encyclopedia of Traditional Symbols" by J.C. Cooper