What's the name and purpose of a barrier raised behind a carrier based jet?
The official name is a Jet Blast Deflector.

As the name suggests, they direct the fast-moving and hot air from the jet engines upwards. This protects the personnel and equipment behind the departing aircraft from getting blown around or damaged from the jet blast. Because of the high temperature of the jet blast, they may have active cooling systems, and must be allowed to cool sufficiently before being used as regular deck again.

To illustrate the risks, see this video, which shows a vehicle being blown away by a 747.

There was also a recent event in Pakistan where a 737 damaged the tarmac (and, as a result, itself) during an engine run-up.

To make a comparison, each engine on a 737-400 can produce up to 22,000 lbf (98 kN) of thrust. The Su-33 in your picture has two engines close together which can each produce 16,750 lbf (74.5 kN) of thrust, or 28,214 lbf (125.5 kN) with afterburner.  That's a total of 56,248 lbf of thrust in afterburner, or 2.5 times the force of one engine on the 737-400. Of course, this does not directly equate to jet blast or temperatures, but it is a good indicator of the forces involved.

To provide a better idea of the jet blast, see this chart (based on the 737-800). At 20 m behind the tail (which is about 20 m behind the engines), the jet blast can reach 300 km/hr at takeoff thrust. For more details about jet blast on the 737 series, see the Boeing documentation.

The CFM56-3 (used on the 737-400) can produce exhaust gas temperature (EGT) of up to 930 C at takeoff. This will mix with the cooler bypass air (and ambient air) to reach cooler temperatures further behind the engine. Military jet engines have a smaller bypass ratio, which means there is less of the cool bypass air in the exhaust to mix with the hot core exhaust.