"Nuclear lightbulb" is the nickname given to a type of gas core nuclear thermal rocket that makes use of a closed cycle in order to address one of the worst problems with the typical GCNTR.
In a normal GCNTR, the core of the rocket, its nuclear reactor, is a cloud of 235U-hexafluoride gas, which is kept rotating to reduce the amount of fuel lost in the exhaust. However, for a number of reasons, it's impossible to completely prevent uranium and highly radioactive fission fragments from leaving the rocket in its exhaust. This isn't a problem in space, but it makes the GCNTR utterly unsuitable for takeoffs, for much the same reason as the nuclear saltwater rocket. The nuclear lightbulb attempts to address this by containing the reacting UF6 gas inside a fused quartz vessel which then cools by radiation, transferring its heat to the rocket's propellant, which is usually hydrogen.
This prevents any radioactive material from being vented overboard, but at the cost of reducing the rocket's exhaust velocity by roughly half. This also halves its specific impulse, meaning that the rocket needs considerably more propellant for a given amount of delta-v. This cuts into the craft's final payload badly, which is a shame considering that surface-to-orbit launches are where this engine would be the most useful. Because it generates three to seven times the exhaust velocity of a chemical rocket, however, it's still an improvement over current heavy-lift systems, even considering its lower thrust.
The biggest problem with the nuclear lightbulb design at present, is that designing a reaction vessel that will actually survive being used is one hell of an engineering feat - near and possibly beyond the limits of modern technology. There are some end runs around this, most of which hinge on the fact that while the engine has to run at a very high temperature to be efficient, this doesn't necessarily translate to large amounts of heat (as measured in joules) per reaction vessel. If done right, the propellant can cool the vessel faster than it heats to its melting point - but this is distinctly nontrivial.