(Favorites have improved in the three years since I first addressed them, so the post should improve too.)
Favorites are preset configurations of the tools. They enable you to quickly configure a tool for a given purpose, like option-clicking without the need for a placed element.
Our default favorites are limited to a handful of most basic presets for each tool. Too many favorites is no better than wide-open tools.
You can access favorites in two ways.
First, there's a 'Favorites' button at the top left of the settings box. Select the one you want, then click 'Apply.' No double-click. Rats. You can also create a new favorite through this box, by setting up the tool and clicking the button at the top.
Second, you can display the Favorites palette at Window | Floating Palettes | Show Favorites, Or Ctrl+F. Here, you can double-click a fave to activate the tool with those settings. (I prefer the palette method and keep the palette open most of the time.) On the flyout at the top right, there are more options for managing the faves:
• Delete or rename an item.
• Save a new favorite based on the current default tool settings, or on the last element selected.
• Redefine an existing favorite with the default or selection settings.
• Save favorites: Export the favorites list as a file.
• Load favorites: Here.
• Favorites Preferences: Show favorites of active tool only? Definitely. Parameter exclusion? Yes, some.
Related: Clearing the Favorites