What are condoms made of?

Condoms are usually made of latex or polyurethane. If possible you should use a latex condom, as they are slightly more reliable, and in most countries they are most readily available.
Latex condoms can only be used with water based lubricants, not oil based lubricants such as Vaseline or cold cream as they break down the latex. A small number of people have an allergic reaction to latex and can use polyurethane condoms instead.
Polyurethane condoms are made of a type of plastic. They are thinner than latex condoms, and so they increase sensitivity and are more agreeable in feel and appearance to some users. They are more expensive than latex condoms and slightly less flexible so more lubrication may be needed. However both oil and water based lubricants can be used with them.
It's not clear whether latex or polyurethane condoms are stronger – there are studies suggesting that either is less likely to break. With both types however, the likelihood of breakages is very small if used correctly.
The lubrication on condoms also varies. Some condoms are not lubricated at all, some are lubricated with a silicone substance, and some condoms have a water-based lubricant. The lubrication on condoms aims to make the condom easier to put on and more comfortable to use. It can also help prevent condom breakage.