Damage resistance is how much resistance shields, armour, and structure have against the 4 damage types.
Shields usually have high explosive resistance (around 60%), little to none EM resistance, (usually 0%) and 25-40% for kinetic and thermal.
Armours have low explosive resistance (0%), high EM resistance (usually 60%) and 25-40% for thermal and kinetic.
Structure has 0% resistances all across the board, and so is useless for tanking.
Damage resistances can be increased by skills, ship bonii, armour hardeners, shield hardeners, and damage controls.