Carrying a spare tube is a must do if you cycle often or commute. There is nothing that frustrates more on a ride than getting a puncture, especially one that you cannot repair.
There are 2 main types of valves on tubes now, Schrader and Presta.
Schrader valves are the same size valve as your car. A circular valve with threads to the top. The inner core of this valve is removable however your rarely need to do so. This valve is often used on mountain bike tubes and hybrid tubes.
Presta valves are also called high pressure valves. They are thin and pointy. To pump these up you partially unscrew the valve itself. Then screw it back up after inflation. This valve is used mainly on road bike tubes as well as mountain and hybrid bikes. As some road bike use deep section wheels, Presta valve tubes come in a range of lengths starting with 33m and going up to 80mm with 42mm and 60mm length in between.
Cycle inner tubes are usually made from butyl rubber. The rubber stretches well so it fills the contours of a wide range of tyre widths. It is also repairable using patches and vulcanising glue.
Some brands have some tubes in their range made from latex. This produces a very light tube however latex as a material loses pressure quickly by compares in and so need pumping up more frequently. Due to the level of stretch that latex has you are unable to fix these tubes should you get a puncture and they are fairly expensive in comparative to the butyl tubes so few people use them.