Traditionally, Christmas pudding (or, more correctly, plum or figgy pudding - fig was just a generic term for dried fruit) contained meat. The suet used in Christmas pudding and mincement is a throwback to this practice.
In fact, there still remain some recipes for mincemeat listing finely minced beefsteak as an ingredient. It's believed that the addition of the beef makes for a moister and more succulent mincemeat.
There is probably a common mediaeval root for all preparations of this kind; meat, fat, spices and some sort of filler, be it oatmeal, breadcrumbs or some such, feature in sausages, blood sausages such as black pudding and boudin noir (the words 'pudding' and 'boudin' are, clearly, related), haggis and the members of the plum pudding family They are all soft or soupy mixtures encased in intestine, a stomach or, latterly, a cloth and cooked until they become firm. Recipes similar to these can be found all over the world.
Good black pudding is yummy. Bad black pudding is just nasty. *S*