Paying life means using your life total as a resource to draw cards, cast spells, activate abilities, or gain access to effects that would otherwise cost more mana or other resources. The tradeoff can be extremely efficient as long as you avoid dropping to 0 life.
Ad Nauseam can exchange large amounts of life for cards, while Black Market Connections lets you spend life for cards, Treasure, and creatures. Lifegain can help replenish what you spend and keep these effects sustainable over a longer game.