Low stances are seen in Kong Sang Koon, one-step fighting techniques and several forms I haven't learned yet (I've seen them performed by some of the masters, though, and I look forward to learning them myself). They are designed primarily to sweep the base leg out from under the attacker and therefore usually follow a forward attack.
The key to a good sweep is to come behind the person's leg and hit right at the heel such that the momentum knocks their leg(s) forwards and out from underneath them. If you attack the leg from the front you'll hit the shin and hurt yourself. (Or if you attack the front of the keg with enough force you'll break it, but that's a different technique altogether.)
The most common mistake with this technique is hitting too high up on the leg such that you catch the back of the knee. It'll cause the attacker to bend the knee but it's not going to produce the desired effect. (See below for desired effect.)
The reason this technique is so difficult to perform correctly is usually a lack of flexibility. Getting that low to the ground requires some real strength in the muscles around your knee and hips and requires some serious conditioning on the part of the person performing it. When you do you, however, it can be a pretty powerful technique in terms of ending a fight.
(PHOTO: Eagle Tae Kwon Do)