Can't add to Tinstaafl's excellent explanation of the coriolis force itself. Whirlybird also asked about how you get from there to wind blowing parallel to isobars. Here's a mental model that might help.
Imagine you have a car with slightly slippy tyres, and a fault with the steering that means that it always pulls slightly right (its "coriolis force"). The faster you drive it, the more it pulls to the right.
Start driving it down a slope, like a hillside. It turns to the right. It accelerates, so it turns more to the right, and so on. Eventually it reaches a point where it has turned 90 degrees and is moving directly across the slope -- the force accelerating it down the slope (to the left) is exactly the same size as, but opposite to, the force that's pulling it to the right (up the slope). It's in "equilibrium".
If it were to turn further right, it would be going up the slope, it would slow down, the pull to the right would decrease, and so it would start going downhill to the left again. If it were to turn left, it would be going down the slope, it would speed up, the pull to the right would increase, and so it would start going uphill to the right again.
If it were to slow down, the pull uphill to the right would decrease, it would start sliding down the slope and would speed up again. If it were to speed up, the pull uphill to the right would increase, it would start turning up the slope and would slow down again.
So there's only one thing it can do -- drive along at a particular speed (that's its "geostrophic speed") at right angles to the slope (i.e. along the contours).
If you're not into cars, try thinking of a a skier with heavy backpack on her right hip.
That's what it feels like to be a air packet of the geostrophic wind.
Hope that helps.