Secret Santa is a way of giving gifts anonymously. A group of people put their names into a Santa hat (or another container!) and then everyone pulls out a name at random (if you choose your own name, you have to choose another one). You then buy a present for that person.
When the presents are given out (often at a Christmas party), they are put together, sometimes under a Christmas Tree (so people can't see who left the present). Each person is given their present - but they have no idea which person bought it for them!
There can also be a variation where people have to purchase a present and then, at the gift exchange, names are chosen at random and then the person chooses a present.
Sometimes people will reveal who the 'present giver' was, but it's also common for it to remain a secret!
There's often a limit put the amount you can spend (like $5 or £5) so all the presents are about the same value. Sometimes there's also a theme like food, something homemade, a Christmas decoration, etc.
No one is sure where the tradition of Secret Santa comes from. It might have begun in Sweden with a custom called 'Julklapp' (which means 'Christmas knock'). Several hundred years ago there was a tradition where you would knock on the door of a friend or neighbour and then leave a small gift (often made from straw or wood) on the door step. The gift would have a little motto/riddle with it, to help people work out who had left the gift.
The story of St Nicholas giving money anonymously to a poor family means that he probably really was the original 'Secret Santa'!
Secret Gift Exchanges around the World
Secret Santa type of gift exchanges are now popular around the world - but they're not always called 'Secret Santa' and it's not always 'Santa' who brings the gifts.
In Germany and other German speaking countries it's known as 'Wichteln' - the name for a small Christmas gnome/elf.
In Spain, Portugal and much of Latin America it's called 'amigo secreto' (secret friend). In some countries, like Brazil, amigo secreto can take place all December with small gifts being left and on Christmas Day the amigo secreto reveal themselves!
In the Dominican Republic Secret Santa is known as 'Un Angelito' (a little angel).
If you're in The Philippines, you might have to wait until Epiphany (6th January) when The Three Kings who will bring any presents - including secret ones!
In Israel Secret Santa known as 'גמד וענק' (Dwarf/Giant) and is very popular in schools at Purim - the Jewish festival that celebrates when the Jewish people were saved by Queen Esther. Purim normally takes place during March. The 'dwarfs' give gifts to the 'giants'! Giving gifts and playing games are very popular during Purim celebrations.