2-D electrophoresis begins with 1-D electrophoresis but then separates the molecules by a second property in a direction 90 degrees from the first. In 1-D electrophoresis, proteins (or other molecules) are separated in one dimension, so that all the proteins/molecules will lie along a lane but that the molecules are spread out across a 2-D gel. The two dimensions that proteins are separated into using this technique can be isoelectric point, protein complex mass in the native state, and protein mass.
This technique is most commonly used when trying to establish a proteome for an organism, but can be used to demonstrate changes in expression, in the change in size/concentration of the spot on the gel that corresponds to the target protein.