Lifelink converts damage into life at a one-to-one rate, and the practical consequence is that combat stops being a zero-sum exchange. A 3/3 with lifelink that trades with another 3/3 has still netted you three life; an unblocked attack swings the life totals by twice its power. Against an aggressive deck this can flip a race in a single turn, and against a burn deck it stretches the clock by enough turns to find an answer. The keyword tends to live on midrange creatures, on equipment, and on the kind of high-toughness blocker that wants to soak hits without dying.
What it changes most is the texture of the race. A lifelinker on the board means an opponent cannot simply count power and assume the math holds; they have to either remove it or accept that every point of damage they take is doubled in tempo. It also rewards going wide and going tall in different ways: a single big lifelink swing buys a cushion, while anthem-style lifelink across a board can put the game out of reach in one attack.
The honest weakness is that lifelink does nothing about the board. Life is not tempo; a player at forty against a resolved combo or a sweeper is in the same position as a player at twenty. On a body the opponent is happy to ignore, lifelink is decorative. It shines when the creature was already going to connect, and it embarrasses itself when the creature was already going to die.