The meniscus is a wedge-shaped cartilagenous shock-absorber, which exists between femur and tibia on either side of the joint. Each knee has two menisci.
In the illustration you can see the two menisci between the femur and the tibia bones. For clarity, the cruciate ligaments and quads muscle are removed. The wedge-shaped meniscus accommodates the incongruity between the rounded end of the femur and the flat surface of the tibia.
Each meniscus is curved like a pair of horns - the front bit is called the anterior horn, and the back bit is the posterior horn. The meniscus on the inner side is called the medial meniscus and the one on the outer side is the lateral meniscus.
This next illustration of the front of the left knee shows how the rounded condyle of the end of the femur snugs into the crescentic meniscus.
The inset on the right is a photo taken close-up during arthroscopy, so that you can really see what a meniscus looks like.