The human knee contains two cartilage-like pads each known as a meniscus. Menisci help absorb shock and keep the knee bones from rubbing against each other. They experience general wear and tear over time, and can be injured in the form of tears. As the writeup on the subject notes, a meniscus is generally crescent shaped.
Generally.
If you are in the 1.5-to-three per cent of the population that has a discoid meniscus, yours is either a bit thicker and larger than most people's or much closer to the shape of a circle than a crescent. If medical websites are to be believed, you are at greater risk of a meniscal tear. You may need surgery. You might experience some pain or discomfort, or some clicking or popping in the knee area, even if the meniscus isn't damaged. You might also never have any symptoms at all.
According to these medical resources I've been Googling all afternoon, a discoid meniscus is more common in the lateral, or outside, meniscus than in its medial counterpart.
(I am not a doctor. I had never even heard of a discoid meniscus until about five hours ago, when a kindly receptionist handed me a copy of my MRI report. Based on conversations with my physiotherapist, I honestly thought I was dealing with a torn MCL. It turns out there are no tears anywhere, but the report noted that "there is a discoid meniscus" in my left knee. The doctor doesn't think I need surgery, and we're going to see whether working on my alignment with osteopathy helps. Running is still out, but I'll deal.)
Resources:
http://orthoinfo.aaos.org/topic.cfm?topic=A00570