The most basic, and most commonly used, operation with the dialog is simply to click on one of the gradients in the scrollable list, in order to make it GIMP's current gradient, which will then be used by any operation that involves a gradient.
If you double-click on a gradient, you will be able to edit its name. Note, however, that you are only allowed to change the names of gradients that you have created yourself, not the ones that come pre-installed with GIMP. If you try to rename a pre-installed gradient, you will be able to edit the name, but as soon as you hit return or click somewhere else, the name will revert to its original value. It is a general rule that you cannot alter the resources that GIMP pre-installs for you: brushes, patterns, gradients, etc; only ones that you create yourself.
The buttons at the bottom of the dialog allow you to operate on gradients in several ways:
This button activates the Gradient Editor.
This creates a new gradient, initialized as a simple
grayscale, and activates the Gradient Editor so that you
can alter it. Gradients that you create are automatically
saved in the gradients
folder of your
personal GIMP directory, from which they are automatically
loaded when GIMP starts. (You can change this folder, or
add new ones, using the Preferences dialog.)
This creates a copy of the currently selected gradient. You will be able to edit the copy even if you cannot edit the original.
This removes all traces of the gradient, if you have permission to do so. It asks for confirmation before doing anything.
If you add gradients to your personal
gradients
folder by some means
other than this dialog, this button
causes the list to be reloaded, so that the new entries
will be available.
The functions performed by these buttons can also be accessed from the dialog pop-up menu, activated by right-clicking anywhere in the gradient list. The menu also gives you one additional function: