What are shock diamonds?

These are shock diamonds, the luminous zone that you see in the exhaust, also known by the name of Mach diamonds or Mach Disc.Not just air-crafts, you can also see the shock diamonds formed by space-crafts engines.

"Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, donut tails or thrust diamonds) are a formation of standing wave patterns that appear in the exhaust an aerospace propulsion system, such as a supersonic jet engine, rocket, ramjet, or scramjet, when it is operated in an atmosphere." -Wikipedia 

For a better understanding take a look at this diagram:

As you can see the nozzle is in over-expanded condition and the exit pressure is less than the atmospheric pressure. At the nozzle exit, you get an oblique shock wave. At the plume boundary, the shock waves give rise to expansion fans and you get to see the plume expanding. In the region where flow pressure is equal to the atmospheric pressure, the expansion wave interacts with the plume boundary and the atmosphere tends to compress the flow. There you get a compression fan. And these compression fans generate a normal shock wave(red line). This entire cycle is repeated until the flow pressure equals to the atmospheric pressure.

When the compression of exhaust takes place just outside the nozzle, it causes increase in pressure. This pressure increment causes temperature to rise, as a result of which combustion of un-burnt fuel takes place in these regions and these become more luminous than the surrounding plume. And that’s how you get the diamonds

The region from the nozzle’s exit to the first diamond is called “Zone of Silence”.