Finder opens Terminal when clicking on homedir icon
A directory can become a "Package", if the bundle bit has been set for some reason by either another program, or the user.
"Kind: Package" will then be visible in the "Get Info" window and it can be opened by the application set in the same window.

Some applications prefer (or create) a package instead of a directory, which can be double clicked to open a whole library folder in an application (iPhoto for example). 
It may also make the user think twice to directly access and edit its contents.

To remove the bit from the home directory run the following command in Terminal (to be found in /Applications/Utilities/Terminal.app, or search in Spotlight):

SetFile -a b ~


SetFile is part of the command line tools. Without the command line tools installed, a popup should ask you if you want to download them. Allow this and try again.