A ramrocket is a combination ramjet/rocket thruster.
It consists of a rocket inside a tube with an air inlet of some kind (supersonic or subsonic) at one end, and a supersonic nozzle at the other.
When the rocket is ignited it rams the air in the tube towards the nozzle. This ram effect alone and gives up to 25% more thrust than the rocket alone would give.
In addition, and more importantly, ordinary rockets typically run fuel rich, to give a higher exhaust velocity per unit of fuel. The ramrocket is therefore able to burn some of this extra uncombusted fuel with the ambient air and generate even more thrust.
In practice, this more than doubles the fuel efficiency (ISP), even somewhat past that of a ramjet (ramjets have roughly twice the fuel efficiency of comparably fueled rockets, but usually only a fraction of the efficiency of conventional jet engines, except beyond ~mach 2.5).
The downside to ramrockets is the extra complexity of the air inlet, which must be able to cope with any variation in air pressure and air speeds, and problems with cooling the nozzle and combustion chamber.
The upside to ramrockets is that they give thrust even at zero speed (unlike ramjets).
In practice the extra complexities have not often been worth it; rockets and conventional jet engines have seen much more use.