The celebration is called Karneval, Fasching or Fastnacht - different regions give it different names. It starts with womens' thursday (Weiberdonnerstag), when women are allowed to cut off the tie of any man they encounter! It's followed by mock-serious carnival conventions all throughout the weekend, where the "carnival president" makes a speech called the Büttenrede and a fake army performs dances while the audience get to drink, laugh and sway with linked arms.
On the Monday (Rosenmontag), the country has a day off work and school in order to attend processions where you do more dancing and singing and admire themed floats and costumes. Everybody shouts Helau! or Alaaf! and the children receive sweets which are thrown from the procession - called Kamelle, so if you're ever in Germany at this time make sure you shout the right thing.