Resolution refers to the amount of data used in video specified in pixels. Resolution is denoted as width x height in pixels. Common resolutions are 720 x 480 for standard definition, or 1280 x 720 and 1920 x 1080 for high definition. Because these resolutions have been standardized, it is easier to just reference the height dimension.
It is common for editors to work in a lower resolution when cutting a project, since applications can run more smoothly with less data. After all the changes are made, the editor can simply bring the resolution back to full for the final output of the project.