We are in the process of updating the WebEdit documentation. Though, some of the content below might still be applicable to your needs.
The context menu tool allows you to do actions related to an asset (files, folders and pages) without needing to select it first. This includes editing, moving/renaming, publishing and deleting assets.
On the right of each asset, there is a small downward arrow. When clicked on, this arrow will reveal a drop down menu that displays various editing options.