The memory interface is the size of the bus. That is the connection between the card and its memory.
Its not as easy as a bigger bus is better. If you are comparing like for like then more is always better but memory comes in differing specifications.
On a GPU the common bus sizes are 128/256/384.
Don't know if this will help or b ea little complicated but for what its worth have a read of this http://www.extremetech.com/computing/81778-gddr5-memoryunder-the-hood
Any more questions just ask.