On a bike, your inner tubes are usually ignored - safely hidden under your tyres.
In the sad event that you suffer a puncture, you'll either have to repair or replace the inner tube.
Carry a spare inner tube with you and you can repair the punctured one at the cafe stop or when you get home.
Better still, fit some puncture-resistant tyres!
Bike Inner Tube Valve Types
Modern bicycle inner tubes use two types of valves...
Presta Valve Inner Tubes
Presta valves are the most suitable valve for high pressure bike tyres. Use a long stem presta valve if you have deep "aero" rims.
Schrader Valve Inner Tubes
Schrader valves (same as a car valve) are usually found on low to mid end MTB and hybrid bikes. The larger hole needed for a Schrader valve can slightly weaken the wheel rim.
Self-Sealing Bike Inner Tubes
Also known as 'Slime' tubes (Slime is a brand of puncture sealant), self sealing inner tubes contain a liquid which fills the puncture and then sets on contact with air. They'll work for pinprick punctures but if your tyre is badly gashed - you'll have a gooey mess on your hands.
Lightweight Inner Tubes
Lightweight inner tubes are probably the cheapest performance upgrade for your bike.
Lightweight tubes are usually made of latex or very thin butyl rubber. Latex inner tubes do not hold air as well as normal inner tubes so you will have to do a bit more pumping to keep your tyres up to pressure.