"Carat Weight" is simply the weight of the diamond.  

By definition, 1 carat is exactly 200 milligrams.  Since most diamonds sold in the jewelry industry weigh less than 1 carat, the carat is usually subdivided into "points."  There are 100 points in 1 carat, so that a diamond weighing 3/4 carat would be a "75 point diamond."  In summary:

1 carat = 200 milligrams = 100 points

Don't confuse the weight of a stone and its size.  The diamonds proportions are the most critical factor in relation to the physical size of the diamond.  Since optically diamonds are viewed from the top a poor proportioned diamond that is shallow or deep will appear considerably different with the same carat size (very good cut diamonds always have a very good or excellent proportions). Also, don't confuse the carats of a diamond with the carats of a different stone.  Because different minerals have different densities, a 1-carat diamond will have a different volume (a.k.a. size) than, say, a 1-carat ruby.  Another common source of confusion:  The karats used to measure the purity of gold have nothing to do with the carats used to measure the weight of a diamond.  Notice the difference in spelling.

Don't make the mistake of shopping "for the biggest diamond at the best possible price."  You will likely end up with a stone of such inferior quality in clarity, color, and cut that it will simply look "cheap" when your partner compares it to her best friend's diamond.  Side by side a diamond cut that gives the diamond FIRE is crucial.  The difference can be astonishing. Many jewelers claiming to be discount or wholesalers will sell you a diamond at a low price. Most of the time the diamonds will not be independantly certified and there will be fundamental flaws in the diamond cut. When you compare these inferior diamonds to a premium cut diamond like Wholesale Canadian Diamonds brokers will you really see what a WOW stone should look like!

If size or carat weight is your most important attribute, (for many people it is very important) that is perfectly acceptable, but do consider the other 3 Cs especially cut to make sure you understand your tradeoffs.