Just to expand on the above a little bit...
REX (Rapid EXpansion) was a strategy commonly employed in previous versions of Civilization. It basically involved settling cities like crazy until all the land was taken. You could pretty much guarantee a win this way, as land = power (and still does in Civ IV).
However, for Civ IV, the game developers purposely wanted to prohibit most if not all of the sure-fire strategies that had worked in Civ III--
especially REX. So they changed the way city maintenance works so that founding too many cities before your economy could handle it will cripple you.
Generally, then, you have two options, and this ties into your other question about other acronymns and strategies you should know about.
If you run a Cottage Economy (CE) where you improve and work most tiles with cottages to generate more commerce as the game goes on and support your economy, then you should try to follow the "60% rule". This rule (though it's more of a guideline, really) says that you should expand until you have to pull the research slider back to 60% to break even or stay in the black. Once you hit that point, build up your economy until you can handle more expansion. The CE is better for beginners such as yourself.
If you run the more advanced Specialist Economy (SE), you can get away with more expansion, because you can allow the slider to go down to 0% in order to break even/stay in the black. You're going to rely on specialists to make up the difference.
Shameless self-promotion: I describe all of these things in more detail my Beginners' Guide (link in my sig).
