1:2 means the image projected on sensor (or film) is up to half the size of real subject; 1:1 means it's up to exactly the same size as the real subject. So yes, 1:1 means you can take a more close-up shot. The ratio in technical specifications means the maximum magnification, you can magnify less by focusing from further away (or zooming out, if the lens is a zoom).
Approximate minimum size of subject that you can fill a frame with (using minimal focusing distance for the lens, and longest focal length for a zoom lens):
- magnification ratio 1:1 - 24 x 36 mm on full-frame, 16 x 24 mm on APS-C
- magnification ratio 1:2 - 48 x 72 mm on full-frame, 32 x 48 mm on APS-C
You can get even higher magnification by adding bellows or extension tube(s) between your camera and lens.
A serious macro shooter may want to consider a Canon system, because they have the MP-E65 lens with insane 5:1 ratio - subject is magnified 5 times compared to its real-life size.
The greater the magnification ratio you use, the thinner will be your depth of field.
As @jrista commented, many people consider only 1:1 or higher magnification lenses to be true macro lenses, while marketers will happily stick "macro" on any lens that will focus closer than lenses of similar focal length usually do.