A creature that has resistance takes less damage from a specific damage type. For example, a creature that has resist 10 fire takes 10 less damage whenever it takes fire damage.
Against Combined Damage Types: Your resistance is ineffective against combined damage types unless you have resistance to each of the damage types, and then only the weakest of the resistances applies. For example, if you have resist 10 lightning and resist 5 thunder and an attack deals 15 lightning and thunder damage to you, you take 10 damage, because the resistance to the combined damage types is limited by the lesser of the two resistances.
Not Cumulative: Resistances against the same damage type are not cumulative. Only the highest resistance applies. For example, if you have resist 5 cold and then gain resist 10 cold, you have resist 10 cold, not resist 15 cold. Similarly, if you have resist 5 cold and then gain resist 2 to all damage, you still have resist 5 cold, not resist 7 cold.
Published in Monster Manual 2, page(s) 218, Monster Manual, page(s) 282, Player's Handbook 3, page(s) 222.