A topping lift is a line that usually runs to the top of the mast and is used to support a boom, or other spar.
Many sailboats use a topping lift to support the boom to keep it from hitting the deck (or people's heads) when the mainsail is not raised. When the mainsail is hoisted, the sail should support the weight of the boom and the topping lift should go slack. Some sailboats use a spring-loaded vang system that supports the weight of the boom so a topping lift is not needed.
A topping lift is also usually used to support the weight of a spinnaker pole when it is deployed.