Diamonds are measured in a unit of weight called "Carats". A carat is subdivided into 100 points and weighs 0.2grams. Therefore a diamond that weighs 0.1grams is a half carat or 0.50ct.
Because diamonds are measured by weight rather than size, a 2.0ct diamond is not going to be twice the size (diameter) of a 1.0ct diamond.
The table below shows relative diamond sizes by carat. This table is not to scale since computer monitors vary in resolution and would be aproximate in any case. It will show you relative size differences though.
The weight of a diamond is the largest factor in determining the price of a diamond. If you like larger diamonds and jewellery in general, but are constrained by budget, then picking a diamond of slightly less clarity or colour can bring down the price and it is still possible to have a stunning looking diamond.
When picking a diamond for a ring remember that slender fingers make a diamond look bigger.