There are many types of speakers available for different applications. So how do you choose which ones to buy?
The first thing to consider is how you want to use your sound system. Are you looking for a portable sound re-enforcment for your band or solo act, or are you wanting an installed system in your shop, school or office?
Typically, portable speakers are described as 12" or 15" and, if they are passive, are described as low impedence (usually 8 Ohm, sometimes 4 Ohm - this information is important for matching a suitable amplifier). Installed systems within shops or offices are likely to consist of 100v line ceiling or small wall mount speakers. Using 100v systems allows many speakers to be chained together and run from the same amp. This isn't possible with low impedence systems where the maximum number of speakers per amp channel is usually 2 or possibly 3.
Active / powered speakers have an amplifier built in. This makes a system very easy to set-up and use as you don't have to worry about using a seperate amplifier. Manufacturers spend lots of money on research and development, building a matching amp to their speaker so you can be sure that you'll get the best performance your system is capable of.
Passive / unpowered speakers require a seperate amp. This makes them lighter to carry and has the advantage that a power supply is only required for the amp, rather then having to have one for each speaker. It does bring the problem of making sure the amp is a suitable power rating for the louodspeakers - this is made trickier as manufacturers advertise different ratings for their products, usually to try and make then appear better then they actually are.