Double strike is a combat ability that lets a creature deal damage twice in the same combat. It deals damage during the first-strike combat damage step, just like a creature with first strike, and then it deals damage again during the regular combat damage step. The reminder text says it plainly: the creature deals both first-strike and regular combat damage.
That matters because a double-strike creature can hit before most other creatures hit back, often killing a blocker before it deals any damage. If it isn't blocked, it deals its power to the player or planeswalker twice, effectively doubling its combat damage. Abilities that trigger on combat damage, like lifelink or whenever this deals combat damage, also trigger twice. It's a strong keyword for winning combat and closing games quickly.
