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To discuss the role and use of coatings, it is necessary to first have a look at a gas turbine (below, a jet engine) and get an idea of the different problems the materials encounter.

A jet engine (Rolls-Royce Trent 800), showing the different stages: intermediate pressure compressor (IPC), high pressure compressor (HPC), high pressure turbine (HPT), intermediate pressure turbine (IPT), low pressure turbine (LPT), and the pressure and temperature profiles along the engine.
Image of the Trent 800 courtesy Rolls-Royce Plc. Diagrams after Michael Cervenka, Rolls-Royce.

An excellent and simple description of the functioning of a jet engine can be found on the Rolls-Royce website: Journey through a jet engine. General Electrics also has a slightly more detailed yet fun demo. Land-based gas turbines as used in the power generation industry are in principle very similar, but larger, and the actual turbine (the last rows of blades in the engine) is not connected with the rest of the engine, but drives a generator. In some cases however, a first turbine does drive the compressor, while a second is connected to a generator (power generation) or power shaft (marine engine).

A gas turbine for marine propulsion, with a two-stage turbine, the first one driving the compressor, the second providing the power. From this page

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