They play and tap land cards for mana, allowing them to cast spells. Spells come in a number of categories. Creatures are what you summon to battle with your opponent's creatures- if a creature attacks and no opposing creature blocks it, it does damage to your opponent. If an opponent loses all of his 20 life, he's out. Sorceries and Instants have powerful one-shot effects like gaining life or destroying creatures.
Rules summary over.
The official 'setting' for the game is Dominia, a multiplanar universe, and Dominaria, one of the worlds in that universe, is often the focus. Right now the game's slogging towards the end of a huge multi-expansion storyline about an evil plane called Phyrexia planning to invade Dominaria by way of the artifical plane of Rath. Things get complicated. Well, most of them are interesting. Gameplay itself is quite strong.