A creature with ward demands a toll before the opponent can touch it. Point a removal spell at it, target it with a bounce effect, aim a Doom Blade: first you pay the tax, in mana or a card or some life, or the spell is countered outright. The threat is still answerable, but answering it costs more than the answer was supposed to cost. Ward turns clean one-for-ones into awkward two-for-ones, and it punishes the kind of efficient interaction that decks are built around.
What ward really does is buy a turn. Against a removal-heavy opponent holding mana up, the tax often means the creature resolves, untaps, and gets to attack or trigger once before they can pay both for their spell and its surcharge. That single extra turn is frequently the entire game with a planeswalker, a value engine, or a commander the deck is built to chain off of. It lives most naturally on midrange threats expensive enough to deserve protection but not so expensive that protecting them is redundant.
Its ceiling is set by what it cannot do. Ward does nothing the turn the creature enters, nothing against a sweeper, and nothing against a sacrifice edict or a -X/-X effect that never targets. It is also dead weight on a body the opponent was happy to ignore. Ward protects the threats that draw removal, which means it is best on creatures that would otherwise eat it twice.