Christmas is celebrated to remember the birth of Jesus Christ, who Christians believe is the Son of God.
The name 'Christmas' comes from the Mass of Christ (or Jesus). A Mass service (which is sometimes called Communion or Eucharist) is where Christians remember that Jesus died for us and then came back to life. The 'Christ-Mass' service was the only one that was allowed to take place after sunset (and before sunrise the next day), so people had it at Midnight! So we get the name Christ-Mass, shortened to Christmas.
Christmas is now celebrated by people around the world, whether they are Christians or not. It's a time when family and friends come together and remember the good things they have. People, and especially children, also like Christmas as it's a time when you give and receive presents!
No one knows the real birthday of Jesus! No date is given in the Bible, so why do we celebrate it on the 25th December? The early Christians certainly had many arguments as to when it should be celebrated! Also, the birth of Jesus probably didn't happen in the year 1 but slightly earlier, somewhere between 2 BCE/BC and 7 BCE/BC, possibly in 4 BCE/BC (there isn't a 0 - the years go from 1 BC/BCE to 1!).
The first recorded date of Christmas being celebrated on December 25th was in 336, during the time of the Roman Emperor Constantine (he was the first Christian Roman Emperor). But it was not an official Roman state festival at this time.