Kicker is an optional additional cost you can pay when casting a spell, usually for an extra effect. The card says "Kicker [cost]"—if you pay it as you cast the spell, you get the bonus described by text like "If this spell was kicked..."
The biggest misconception: you choose to pay kicker when casting, not later, and it's part of the spell's total cost—so it can't be paid after the spell's on the stack. Multikicker lets you pay the kicker any number of times for a scaling effect. Importantly, kicked spells aren't a different spell type; they still get countered, copied, or redirected normally. Copies retain whether the original was kicked, but copies don't let you pay kicker again.
In Commander, kicker shines with big mana ramp—late game, those kicker costs turn modest spells into bombs, giving flexible early/late-game versatility.