ALL speakers need an amplifier (AMP) to be heard. Mic levels are very small signals, Line levels from turntables, CD players, computer output, etc are bigger but still are not big enough to run the speakers. If you are a DJ you will want some nice speakers to really move the audience. The AMP is what boosts those mic and line level signals up to where they will drive a speaker.
Your DJ board where you MIX may have an amplifier built-in. Look to see whether it has "LINE OUT" (usually a little plug called a phono jack) or "SPEAKER" outputs (sometimes labeled 8 ohm, or 8 and then a greek omega character [like an upside-down pot] which stands for ohm. These are usually 1/4th inch holes with a plug that is about 1.5 inches long)
If your mixer has "LINE OUT" plugs you need to connect them to "LINE IN" of an amplifier. This amplifier would have on/off, volume, and bass/mid-range/treble adjustments on the front. The speakers would connect to "SPEAKER" jacks on the rear. Occasionally, they will have a banana plug or a weird connector called a speakon connector. Get a picture at:
http://accessories.musiciansfriend.com/product/Monster-Cable-S100-Speaker-Cable-with-Speakon-Connectors?sku=331642
The strong signals coming out of the amplifier drive the speakers.
Powered speakers are amplifier/speaker combinations in the same box. You connect "LINE IN" to the powered speaker and it amplifies it and feeds it to its' own speaker. They are a combination and this is why they are more expensive.
One advantage to powered speakers is that the amp and speaker are matched in power. You don't have a small amp struggling to drive speakers too big for it. You don't have speaker coils getting fried by an amplifier too powerful for them. It is also one less thing to pack if you are a traveling DJ.
Hope this helps.