In an adiabatic process, no heat is transferred:   dQ = 0.

Examples: Fast processes where there is no time to transfer heat (e.g., an engine).
An insulated system.

For an adiabatic process, the First Law gives:  dE = + dW.

In expansion, a gas does work; the environment does negative work on the gas, dW < 0.

Thus an expanding gas cools in an adiabatic process.

The equation governing an adiabatic path (adiabat) in the P-V diagram is:  

PV^γ = constant   or, equivalently,   TV^γ-1 = constant.