Mince Pies, like Christmas Pudding, were originally filled with meat such as lamb rather than a dried fruit mix as they are today. They were also first made in an oval shape to represent the manger that Jesus slept in as a baby, with the top representing his swaddling clothes. Now they are normally made in a round shape and are eaten hot or cold. I like mine hot with some ice cream!
On Christmas Eve, children in the UK often leave out mince pies with brandy or some similar drink for Father Christmas, and a carrot for the reindeer.