In an automotive application, understeer is when the vehicle turns less than you think it should for the amount of steering wheel input. Exagerated case: you turn the wheel a lot but the vehicle only turns a little.
Oversteer is the opposite, where the vehicle turns a lot for a little input.
Most cars are designed to understeer, as this is considered safer for average or poor drivers.
Applying power while cornering can greatly reduce understeer on a rear wheel drive car.
Can't remember his name, but some old-time NASCAR guy summed it up like this...
"Understeer is when you hit the wall with the front of the car, and oversteer is when you hit the wall with the back of the car."
Actually, my car exhibits characteristics opposite of what Dave holds to be true. If I apply throttle in a minimal adhesion situation, the front of the car wants to skid. If I enter a turn too hot and chop the throttle, the rear end will swing around. The latter is known as "lift throttle oversteer" and is a common trait in cars with 50/50 weight distribution or rear-engined cars.
If you have Speedvision, I recommend watching the Superbikes and Grand Prix bikes closely as they enter and exit the turns. You will pick it up quickly. Exciting stuff, if you know what to look for...
I think automotive dynamics are of limited relevance in terms of over/understeer in MX.
The most common situation where I have understeer is entering flat turns while still decelerating. It feels like your front tire is sliding out from under you, and is not very nice.
The most common case of oversteer occurs when I gas it out of a corner. The rear steps out. This is often pretty cool, but usually not fast.
Body positioning greatly affects over/understeer, too little weight in the front increasing understeer and vice versa.
Braking and throttle use are more complicated as to their effects. When you apply throttle, you transfer weight to the back as the rear suspension compresses, thus increasing the chance of understeer. However, you are also now using some of the rear tires tractive capacity to accelerate, leaving less for lateral forces, inducing oversteer. You can deduce how braking at both ends affects these.