Modern jet engines, are of the high bypass turbo fan type.
In these designs, a small core compresses air, and then mixes this air with a fine mist of jet mist of jet fuel, and ignites the mixture. A high speed stream of hot exhaust gasses then flows over the rear turbines, and spins up the main large fan at the front of the engine.
This main front fan sucks in a significant mass of air, and redirects this cold air around the smaller internal engine, bypassing the combustion chamber (hence the name high bypass engine)
On modern turbofan engines, up to 80% of the thrust produced is cold air thrust!
When this hot and cold air exhaust meet at the engine outlet, they posses different densities and do not mix well. This creates a large amount of noise, and unwanted vibration (felt as wasted energy, and thus drag).
The idea of the chevrons is to help mix the hot and cold flows, and therefore reduce the operating noise of the engine.
Perhaps a slight simplification, as there is some pretty advanced fluid dynamics going on, but the main idea is to help mix the hot and cold exhaust flows to reduce noise.
Source: QUORA
