Cartilage is a substance that adds to the structure of the body by being somewhere between stiff and flexible - something to be used when you want something to have a bit of bend in it, but also to be pretty solid. Bones are important for forming the structure of the body, but sometimes you need something more flexible - for instance, at joints; that's where cartilage comes in.
It's made up of two major parts: cells and the gloop that surrounds them. Although 'gloop' isn't the official term, it's helpful to think of lots of cells surrounded in this substance which they're producing - a bit like bees, merrily producing honey all around them. The cells are known as chondrocytes, and the stuff around them is the extracellular matrix - a kind of noodle soup, made up of collagen and elastin fibres in a proteoglycan-rich mixture.
The recipe used to put together this soup determines what kind of soup you're going to get - so different amounts of the noodles leads to a different type. There are three types of cartilage, each with a slightly different recipe to change the way that the cartilage acts. These three are hyaline cartilage, fibrocartilage and elastic cartilage.
A chondrocyte is a cell which you can find in the cartilage. It's job is to produce the extracellular matrix - the noodle soup - which surrounds it. Chondrocytes are cousins of the cells which produce bone, but while they're both involved in the manufacturing business, only chondrocytes can produce cartilage.
In fact, the only cells you're going to find in cartilage are chondrocytes - other cells just stay clear of it. That's mainly because you don't really need many cells in cartilage - and it would be a problem if you did. There are no blood vessels running through cartilage, so that only way that any cells have the energy to keep going is if oxygen and nutrients diffuse across the noodle soup between cells.
Hyaline cartilage is a firm but flexible substance that you often find when cartilage is on its own, or at the end of bones in synovial joints. It's the same stuff that you get at the end of chicken drumsticks that I used to call 'gristle' - too soft to look like bone, but too tough to eat. It's called hyaline (meaning 'glassy') because it has a shiny appearance like glass.
Your nose, costal cartilages (in the ribs) and the tough rings supporting your trachea (windpipe) are all made out of hyaline cartilage. If you press on your nose, you can feel how firm it is. The key thing about hyaline cartilage is that it's made up simply of cartilage cells (chondrocytes) and the noodle-soup matrix which surrounds them. In the case of hyaline cartilage, this noodle-soup is made with a recipe that uses mainly collagen (Type II) and chondroitin.
There are no blood vessels or nerves that go through hyaline cartilage - oxygen and nutrients just need to diffuse through in order to feed the cells. The closest oxygen and nutrients can get is the surrounding layer - usually a thin membrane which surrounds the cartilage called the perichondrium. However, if the cartilage is already surrounded in skin, it doesn't need the perichondrium. You'll also find that it doesn't have this layer around the ends of bones in joints.
Fibrocartilage is, rather obviously, a type of cartilage with a lot of fibrous tissue in it. This makes if very tough - but, because it's still cartilage, it's still a bit bendy. All of the bundles of collagen (and other noodle-soup proteins) are arranged around the chondrocytes. This is the kind of set up that you'll find in secondary cartilaginous joints (or symphyses), such as the pubic symphysis.
Interestingly, it's the only type of cartilage that has type I collagen as well as type II.
Like hyaline cartilage, elastic cartilage is a type of cartilage filled with chondrocytes, Type II collagen and chondroitin. However, unlike hyaline cartilage, the main protein in elastic cartilage is (surprise, surprise) elastin. Elastin is a protein which is very bendy indeed - but which will return to its original state. Your outer ear is made out of elastic cartilage, covered in skin, and you can bend it very easily without changing its shape permanently. Elastic cartilage is also the type of cartilage found in the epiglottis.