Hat compatible refers to the standard developed by the Pi Foundation for add on boards, and yes HAT it is an acronym for Hardware Attached on Top. You can read more about it here. The release coincided with the move to 40 pin boards B+. Quoting from the page linked above:
In a nutshell a HAT is a rectangular board (65x56mm) that has four mounting holes in the (nicely rounded) corners that align with the mounting holes on the B+, has a 40W GPIO header and supports the special autoconfiguration system that allows automatic GPIO setup and driver setup. The automatic configuration is achieved using 2 dedicated pins (ID_SD and ID_SC) on the 40W B+ GPIO header that are reserved for an I2C EEPROM. The EEPROM holds the board manufacturer information, GPIO setup and a thing called a ‘device tree‘ fragment – basically a description of the attached hardware that allows Linux to automatically load the required drivers.
So yes it is more than the 40 pin connector it includes the size and location of the mounting holes, how the board and its capabilities are identified and software is configured.
It remains to be seen if and how this changes given the recent release of the Pi zero which is much smaller than the size of current HAT standard.