When someone connects to Desktop Sharing on your machine, you will get a pop-up notification that looks like the following screenshot, unless you are accepting uninvited connections without warning.
If you , the client can proceed to authenticate (which requires the correct password for a personal invitation or email invitation). If you , then the attempt to connect will be terminated.
The Allow remote user to control keyboard and mouse check box determines whether this client can only observe, or can take control of your machine.
If the client connection is successful, and used the password from a personal invitation or email invitation, then that invitation is deleted and cannot be used again. You will also get a small pop-up window in the dock, that shows that the connection has been made.