Advent is the period of four weeks before Christmas. The Advent calendar originated in Germany. It consists of a card with 25 little doors, which are opened each day until Christmas. Behind each door there is a Christmas scene and usually a piece of chocolate for the kids.
Christmas Eve is on December 24th. It's the night when Santa Claus (in the USA) or Father Christmas (in the UK) comes and fills the children's stockings with presents.
Christmas Day is on December 25th. People usually go to mass and have a meal together with their family or friends. The Queen gives a traditional speech.
Boxing Day is on December 26th. People give presents to servants and friends. In the UK it's a public holiday. It originated in medieval times, when every priest was supposed to open the alms box and distribute the money or gifts to the poor people.
Twelfth Night is on January 6th. There's a period of Twelve Days after Christmas, during which people gathers with friends and have parties. The "Three Kings' Day" is not celebrated in England or USA.