While in menus, if you are on their friends list, they will have an option to "Quick Join" you. If they mouse over your name in that list, they will see who you are playing, what quest, and who you are partied with (but not their names, just portraits).
In game, using just the friends list, they don't get this extended amount of info, however they will still see who you are playing as (name and class), what quest, and how many people.
Another interesting thing to note, if they are in a game, they cannot "quick join" you, they would have to be invited by you. However, they could leave their game and then quick join without an invitation.
This is all assuming you have the quick join feature enabled. If you do not, they will not have anything to mouse over and see if there are empty slots in your game. You would have to manually invite them at that point.