A creature with haste attacks the turn it arrives. That is the whole effect, and almost every consequence flows from it: the window between casting a threat and using it collapses to zero, which means the opponent loses the turn cycle they would normally have to answer it. Sorcery-speed removal that would have killed the creature on the upkeep instead trades, at best, after damage is on the stack. A planeswalker that was safe behind a tapped board is suddenly in range. A mana creature that taps the turn it enters generates a full extra activation over its life.
Haste is what turns midrange threats into burn spells and what makes recursion loops lethal instead of grinding. It pairs with anything that cares about attacking or tapping immediately: triggered abilities on combat, mana dorks, token swarms refilled after a board wipe. Red leans on it because red's threats are built to die; the keyword guarantees they do something first. On a creature with an enters-the-battlefield effect that does not need to attack, haste is closer to filler.
The honest ceiling is that haste does nothing on a body the opponent is happy to block. A 2/2 with haste into an untapped board is a 2/2; the keyword sells the first hit, and if there is no hit, there is no sale. It is decisive on evasive threats and finishers, and a rounding error on ground creatures the defender outclasses.