They give you a popup menu of commands that are often used. To activate the menu you click on something while holding down the control key . Depending on what you are clicking the menus will vary. This is what a contextual menu brings up in the Finder. On a folder You will notice that many of the commands are available from the menu bar, contextual menus allow you an easier way to access these commands.
Many programs have commands in the contextual menus that only appear there.
You can add items to your CMs to customize them the way you would like. Many applications now support CMs and come with CM files which offer you commands that are particular to that application. To add a CM file that you have found, or to remove one that you don't want, you place it into the Contextual Menu Items Folder , which is in the System folder , and restart your Mac. You can also just drop it onto your closed System folder and click OK when the dialog box comes up asking if it should be placed in the Contextual Menu Items Folder. Then restart your Mac.