VASIMR is an acronym: VAriable Specific Impulse Magnetoplasma Rocket.
VASIMR is a form of ion/plasma drive being designed by NASA. The basic concept is that a gas, such as hydrogen, which is ionised and heated to millions of degrees centigrade. It's held in place with a magnetic field- necessarily, as nothing solid or even liquid could withstand that temperature! The magnetic field is generated by superconducting magnets, with a strength of around 3 Tesla, that's about 1 million times more intense than the earths magnetic field. It then goes out through a magnetic throat and pushes against a magnetic nozzle, achieving an exhaust velocity of upto 300km/s.
This is a hugely faster exhaust speed than conventional rockets can achieve- they're more like 4.5km/s, or Hall effect thrusters that are about 15km/s or even ion drives such as used on DS1 that work at 30km/s.
Sounds great! Unfortunately not all in the garden is rosy. The energy for all this whizzy exhaust gas has to come from somewhere (in fact, it also goes somewhere- if you run the physics equations more than 99% of all the energy you put in ends up in the exhaust, not the vehicle where you really want it.) Using so much power saves fuel; but it's not completely clear that we need to save fuel quite that much. At some point the power source weighs more than the fuel would, and this is really seriously starting to happen here.
To help this, putting the V(ariable) in VASIMR, when you want to (near to the earth for example) you can 'change gear' and set the exhaust velocity down to 30km/s. That requires 10x less energy, but also 10x more fuel, but also gives 10x more thrust.
Ok, but let's look at the power source. Solar panels have been used before for space drives (see DS1), but that's just a few kilowatts, we're talking megawatts of power here.
The only thing that can supply that much power is nuclear power. There's two problems with that. First, no nuclear reactor exists that can supply that amount of energy in a space situation- the mass of the reactor is likely to be very high, and it's not especially easy, it will cost a lot to design and construct. Secondly, the political issues; quite a lot of very vocal people hate the idea of nuclear power whizzing around above their head. It's silly, the systems can be designed to be, for all intents and purposes, entirely safe to build, launch and operate, but the political opposition can tend to sound the death knell to this kind of project.
And that's a shame really. This drive could probably cut the trip to mars from being a 9 month trip down to being about 40 days or so.
Still, at the end of the day, the VASIMR drive seems to be a short-term solution to the short-term problem, that of high launch costs of fuel in 2002. This makes fuel expensive to launch; and the VASIMR rocket is trying to minimise the amount of fuel that is launched. Long term mining of in-situ resources around the solar system is very likely to mean that the VASIMR concept will be obsolete; and launch costs should be going down as space is being used more and more.
By way of contrast, the Russian researchers are trying to lower the exhaust velocity of Hall effect drives...
Still, VASIMR is a very cool concept.