While it's encouraged by some Christian denominations to give up something for the duration of Lent, it is by no means an obligation, at least for Catholics.
That's only currently. In times past, Catholics were forbidden to eat meat, foul, fat, eggs and dairy products, not only for Lent, but for advent as well. At one time, it was forbidden to eat anything at all between sunrise and sunset (like the Moslem Rammadan fast). The doughnuts/pancakes are about using up all the fat and eggs before the fast, Easter eggs and ham are about being allowed to eat them for the first time in seven weeks, and the St. Martin's day Goose was the last time you could eat meat before Christmas day. Plus no singing, dancing, entertainment of any sort, colorful clothes, musical instruments and just about any kind of fun was allowed during this period, which is why carnevals like Mardis Gras, and in Poznań, St. Martin's Day, were such big deals. Even statues, pictures and mirrors had to be put away or covered with dark cloth, even at home. Bells could not be rung. In church, a wooden clapper was used instead of communion bells during Lent.
Overtime, the rules got laxer and laxer.