A turborocket is a type of aircraft engine combining elements of a jet engine and a rocket.
Once a jet engine goes high enough in an atmosphere, there is insufficient oxygen to burn the jet fuel. The idea behind a turborocket is to supplement the atmospheric oxygen with an onboard supply. This allows operation at a much higher altitude than a normal engine would allow.
Functionally, the oxidizer is added to the engine either directly in the flameholders or it is injected into the engine at some upstream point in the airflow.
The turborocket design offers a mixture of benefits with drawbacks. It is not a true rocket, so it cannot operate in space. Cooling the engine might be troublesome since many turbojet engines require significant cooling air to prevent overheating (melting) crucial parts.
Note that there are several other systems for extracting oxidizer from the air as well, designs known as LACE.
