What you are referring to is air that is taken from the compressor section of a turbine engine for uses other than engine operation. This is referred to as "bleed air." Bleed Air is used for lots of stuff: Running the air conditioning and pressurization, starting the opposite engine (sometimes), pressurizing door seals (on some airplanes), powering deicing/anti-icing equipment... The list goes on.
Hope that answers your question.