A Great Ball is used to attempt to catch a Pokémon with double the original Catchability (up to a max of 100%). During the "Catch That Pokémon" scene, if the player fails the first attempt, they are given the choice to spend 2500 Coins (3500 on Mobile) for subsequent attempts using Great Balls. The player can continue purchasing them for additional attempts, as long as they have enough Coins and the Pokémon has not escaped.
Sometimes, a "Super Catch Power" can occur, which boosts the catch rate even further by a random flat amount. This amount can be substantial especially if the original catch rate was very low. It may be a good idea to hold off on spending coins on a Great Ball until a Super Catch Power occurs for an even better chance at catching the Pokémon.