Hi Riya - I don't think there are any really traditional gifts for giving at Christmas. There may be some differences in other countries but mostly here in the UK we give what we think is appropriate for each person - and what we can afford.
As Christmas is a Christian festival and based on the birth of Christ - if you wanted tradition you could look to the biblical account of the gifts the baby Jesus was given - Gold, Frankincense and Myrrh. These were the kind of valuable gifts you would give a king or prince. Gold, a precious and beatiful metal, Frankincense, a valuable perfume and Myrrh, a luxurious annointing oil.
I'm sure anyone would appreciate the equivalent gifts in today's society!
Just one other thing - in many countries people do not exchange gifts on Christmas day itself. In Germany, Switzerland, Austria and other places it is traditional to give gifts on Christmas Eve.