Julemanden can be directly translated to "The Yule-Man" or "The Christmas-man". In modern Danish culture Julemanden is the equivalent of the English Father Christmas although the roots of the character reach into Danish folklore and mythology wherein Julemanden is a mythical character who is said to bring Christmas presents to children in Denmark on Christmas Eve, celebrated December 24.
The main differences to the English Father Christmas is that Julemanden lives in Greenland, loves risengrød which is rice pudding with cinnamon-sugar, and a slice of butter on top, and is assisted by nisse which are the Danish version of elves.
Julemanden is a relatively new phenomenon in Denmark, appearing some time after World War 2. Until then, there was "Nissefar", "Nissekongen" or "Julenissen" - a character with several resemblances to the modern "Julemand". This tradition is traced back centuries when people believed in Nisser (elves, leprechauns, spirits or mystical entities rarely or never seen directly). Local folklore dictated the expected actions of the Nisser, which could be moody creatures resulting in all kinds of fortunes or even disasters. The role of the "Julenisse" was to bring good fortune to the family and to achieve this, he would have to be treated well especially around Jul (December). This was achieved by feeding him, traditionally with some form of porridge (now rice porridge). If the Nisse was satisfied he would bring good fortune in the coming year.
The gift-giving Nisse that became "Nissekongen" seems to have drawn influences from the American "Santa", when American culture began making an impact in Denmark, but rather than outright copying him, local traditions were tweaked, eventually resulting in a "Father Christmas" type character with only traces of the original "Nisse" and in some respects indistinguishable from "Santa". The "Julenisse" is still, however, "celebrated" and he acts as a stand-in for "Julemanden" in early december, to entertain the childish mind, bring small gifts and sometimes plays tricks on the household, kindergarten etc. where such "creatures" can prosper.