Methane gas is highly flammable. When burned, Methane becomes Carbon Dioxide and Water. Both of these things are natural and can be diffused in their natural cycles. Burning the methane gets rid of the methane emission problem of landfills, while also providing Carbon Dioxide and water for the systems of the Earth to use.
What landfill gas capturing stations do is they capture the Methane gas before it escapes the landfill. They burn it to make Carbon Dioxide and water. The combustion of the Methane produces energy which can power an electricity generator. This turns Methane into usable energy for humans.
This is a great video by Waste Management detailing their gas to energy process:
