A creature with vigilance attacks without tapping, which means the same body that pressures the opponent's life total is still standing in front of their counterattack. The practical effect is that combat stops being a choice between offense and defense. A four-power vigilant creature is, on the board, both a clock and a wall, and the opponent has to find an answer that handles both jobs at once.
This rewrites a specific piece of math: the cost of attacking. Aggressive decks without vigilance pay for every swing in exposed life total, which is why midrange mirrors so often stall once both sides have committed their threats. Vigilance breaks that stall in one direction. It turns a creature into a permanent tax on the opponent's attacks, lets planeswalkers stay defended while their protector goes to the red zone, and makes tap effects, whether to crew a vehicle, activate an ability, or convoke a spell, genuinely free rather than a trade against defense. It tends to live on creatures meant to stay on the battlefield: anthem-style lords, commanders, large midrange threats, lifelink attackers whose stabilization only matters if they survive the swing back.
The ceiling, though, is set by the body. Vigilance on a one-power creature is mostly flavor; the thing was never going to change a race or hold a meaningful blocking assignment. The keyword does nothing about removal, nothing about evasion, and nothing on a turn you do not attack. It is a discount on a choice, not a threat in itself.