The basic idea of Magic: The Gathering is that you are a mage who gets power from the land. There are five types of land formations that generate mana, which you can use to cast spells. The five types of mana are red (which comes from mountains), green (which comes from forests), blue (which comes from islands), black (which comes from swamps), and white (which comes from plains).
Your deck has land cards in it, as well as spells. You can play one land card per turn, and you can "tap" your land cards, turning them sideways, to release the mana that you need to cast spells.
You and your opponent each have 20 life points to start with. Using mana to cast spells, you can deal damage to your opponent, and you can block damage that your opponent tries to deal to you, as well as casting spells to improve your ability to survive while hampering your opponent's ability to survive.