It's not only Christians who celebrate Christmas and Easter! The name Easter is actually from the name 'Ēostre', a goddess who is not Christian. Christians celebrate the idea that Jesus rose from the dead at Easter.

I'd refer you to Wikipedia and such, but put shortly and practically, Easter is a Christian holiday for which families gather to celebrate the resurrection of Jesus. It is historically linked to pagan spirituality, so a typical activity is egg-hunting for the children. Someone hides boiled, colored eggs in the garden, so the kids can go look for them (whoever finds the most, wins). Small kids are told that the "Easter Bunny" (or Easter Hare) hid the eggs in the garden. This is a similar mystical creature like Santa Claus. Fun for the family!

Christmas celebrates the birth of Jesus, Easter celebrates the "resurrection" of Jesus. Christians believe than Jesus "Was crucified, dead, and buried: He descended into hell; The third day he rose again from the dead; He ascended into heaven, And sitteth on the right hand of God the Father Almighty." The resurrection is his rising from the dead on the third day. Christmas is always celebrated on December 25th, Easter is celebrated on a date that is calculated in a complicated way and reflects a lunar calendar. Christmas can fall on any day of the week. Easter always falls on a Sunday, "Easter Sunday." In the United States and England, Christmas is culturally rich and complicated and blends elements from many traditions besides the Christian tradition. It is a an important holiday for people of all faiths. The custom of Christmas gift-giving has grown into an important economic and commercial phenomenon. Christmas is the most important secular holiday, If a business ever closes at all, it closes on Christmas. To Christians, Easter is the most important religious holiday. To non-Christians, it is a pleasant but not very important time of year. Because it falls on a Sunday, it is not a work holiday.

Both holidays you mentioned are considered Christian holidays. In reality neither has Christian origins. Christmas was a pagan holiday called Saturnalia that worshiped the Roman god, Saturn. I've heard disagreement about the pagan goddess that Easter is named after; some say Eostre, some say Ishtar, maybe there's another Caananite deity entirely that I have never heard of instead. However, as mentioned earlier, Easter is about the resurrection of Jesus of Nazareth. It is a spring holiday. Historically it was supposed to coincide with the festival of Pesach (Passover and the Feast of Unleavened Bread) because that is when the Resurrection first took place. However, the Catholic church deliberately perpetuated an idea that there is a distinction between these holidays- and this unfortunately stems largely from an ages old, anti Semitic discrimination against the Jews. (The Jewish calendar is lunar based, so the time of Pesach changes that keep it from lining up with the 12 month solar based calendar most Americans are familiar with. It always starts on the 14th day of the month of Nisan, which is the first month of the calendar in Torah. Easter is always on a Sunday, one week after Palm Sunday and ~5 weeks after Mardi Gras and Ash Wednesday.)