An ion drive is a very low thrust, high specific impulse space-only propulsion system.
They typically have to run for months to gain respectable velocity (4-5km/s), but use only a few 10's of kgs of propellent.
The basic principle behind operation is that they take a neutrally charged gas and heat and strip off electrons from some of the molecules in the gas giving a positively charged plasma. The positively charged particles are then accelerated (e.g. by a negatively charged grid) and then exit the space vehicle; recombined with electrons to avoid charge buildup.
The advantage of all this is that very high exhaust velocities can be achieved (30km/s or more) which means that far less propellent is used to give a particular delta-v.
However, this takes energy; a lot of energy. In fact, because the exhaust is so fast, it turns out that the ion drive is very inefficient of energy (nearly all of the energy ends up in the exhaust); but it is very efficient of propellent.
In fact, for high speed exhausts the energy efficiency is inversely proportional to the exhaust velocity, and lower speeds actually gives more thrust for the same energy.
The only known sources that can provide this energy are solar panels (when close to the Sun, atleast out as far as Mars anyway), over a loooooong period, and nuclear.
Current ion drive thrusters such as those used on Deep Space 1 provide very low thrust (the weight of a sheet of paper gives about the same force on your hand), but can be run for 1000s of hours to make up for that. However it is possible to add more thrusters, provided that there is enough power to run them.
Ion drives come in many different flavours; VASIMIR design is possibly the highest performing; and the Russian design MPD is the most flexible and has been flown.