The coilgun is one of the two most common electromagnetic projectile accelerator designs, along with the railgun.
The coilgun consists of a number of electromagnetic coils arranged in a line down the barrel of the weapon. By sending a current through a coil, a magnetic field is formed, and this is used to draw the magnetic projectile towards the coil. Once the projectile is at or near the center of the coil, the current is turned off, and the next coil has its current turned on.
Coilguns have several advantages over railguns, as well as a few disadvantages. First of all, it is a contact-less design. There is no need for the projectile to be in contact with any part of the coilgun while it is being fired, which means that energy loss due to friction is practically non-existant (assuming vacuum in the barrel). On railguns, friction may cause severe problems, and the stress of the acceleration may damage the rails.
Secondly, it can be built to an arbitrarily large size. Among other things, this means that one could build a very large space-based coilgun and use as a mass accelerator even for comparatively fragile implements. The great size of the accelerator would mean that one could reach a high speed without having to resort to a high acceleration.
On the negative side, a coilgun requires fairly sophisticated controls over when the current in a coil is turned on and off, as well as, if we're talking about larger designs, some positively huge capacitors.
There are several other concerns with such implements as well, but as I am far from an expert in the field I will not go in to these and risk huge inaccuracies.