If someone is impulsive, it means that they act on instinct, without thinking decisions through. If you worked for an entire year to save money for a car and then suddenly decided to spend it all on a diamond tiara instead, that would be an impulsive purchase.
Impulses are short, quick feelings, and if someone is in the habit of acting on them, they're impulsive. When stores stock chocolate at the checkout line, they are hoping you will impulsively decide to buy it. When you call the person you have a crush on after promising yourself all day to maintain an air of dignified reserve, that's impulsive behavior. We might also call impulsive behavior whimsical or capricious.