One of the main reasons we have the custom of giving and receiving presents at Christmas, is to remind us of the presents given to Jesus by the Wise Men: Frankincense, Gold and Myrrh.
Christmas itself is really about a big present that God gave the world about 2000 years ago Jesus! One of the most famous bible verses, John 3:16, says: God loved the world so much that he gave his one and only Son so that whoever believes in him may not be lost but have eternal life.
All over the world, families and friends give presents to each other. Most children around the world believe St. Nicholas, Santa Claus or Father Christmas brings them presents, but in Germany, they believe that it is the Christkind, in Spain, they believe it is the Wise Men and in Italy, they believe it is an old lady called Befana.
These presents are also left in different places! In most of Europe, the presents are left in shoes or boots put out by the children. In Italy, the UK and USA presents are left in stockings, often left hanging by a fire place. In many countries, presents for friends and family may be left under the Christmas Tree. In the UK, they are often opened on Christmas day morning with all the family together.
The custom of hanging stockings comes from the story of St. Nicholas.
Presents are opened on different days over the world as well. The earliest presents are opened is on St. Nicholas Day on December 6th. Children in Holland, Belgium, Germany, Czech Republic and some other European countries open their presents on that day.
Children in the UK, USA and many other countries, such as Japan, open their presents on Christmas Day, December 25th. The latest presents are opened on January 6th (a month after the earliest). This is known as Epiphany and is mainly celebrated in Catholic countries such Spain and Mexico.