Replicate is an optional extra cost you can pay when casting a spell. The reminder text says: "When you cast this spell, copy it for each time you paid its replicate cost." So if a spell has replicate {1}{U}, you can pay {1}{U} once to get one copy, twice for two copies, and so on. Each copy is put onto the stack and resolves separately. If the original spell is a permanent, the copy becomes a token.
Replicate lets you turn one card into many, scaling an effect with your available mana. A single spell can become a swarm of copies, which is powerful for effects like damage, card draw, or making creatures. You choose how much to invest, so it works as a flexible mana sink that can overwhelm opponents or trigger abilities that care about tokens entering.
