What Does 'Share and Share Alike' Mean?

Adding to what cindi said, The American Heritage Dictionary of Idioms provides some background:

share and share alike

Mete out or partake of something equally, as in Mom told the children to share and share alike with their Halloween candy. This term, first recorded about 1566, alluded to the equal apportioning of spoils and soon was broadened to include equal sharing in the costs of a venture and other undertakings or possessions.

The Phrase Finder adds that the 1566 cite is to be found in the comedy Damon and Pythias by Richard Edwardes:

Let vs into the Courte to parte the spoyle, share and share like.

It goes on to say that the first recorded appearance of the phrase using the word alike is probably this one from Robinson Crusoe, 1719:

He declar'd he had reserv'd nothing from the Men, and went Share and Share alike with them in every Bit they eat.

Share and everyone gets a piece. Share and share alike and everyone gets a piece the same size.