A diamond's carat rating is a measure of how much the diamond weighs. A metric carat is equal to 200 milligrams. Carats are divided into 100 "points" which allows measurement to the 100th decimal place. Engagement ring centers are typically .75ct to 2ct with more extravagant rings containing 2ct to 6ct diamonds.
The larger the diamond the rarer it is. Certain sizes have big price jumps usually around every .25ct increase. Larger price jumps happen at the whole carat ranges (1ct, 2ct, 3ct...). Given the factors of the other 3C's, bigger is not always better. That said, many people still choose Carat Weight over quality.