Active monitors have built-in amplifiers, so you can hook them up directly to your mixer's Monitor Out. Passives need an external amplifier to drive them.
Make a search on this forum, and you will find many threads covering which monitors people like at different price levels. The Tannoy Reveals (both active and passive) and the JBL 25 something seem to be the most popular entry level monitors. I myself have Alesis Monitor One (Passive) and having worked with them for about five years I know them so well it would really take a lot for me to get rid of them. Like if someone all of a sudden would give me a pair of Mackie 824's.
Cheers
/Henrik