A VSQ is the file extensive that the Vocaloid2 software saves you work in. In the original Vocaloid this was just a standard midi file type and in Voclaoid 3, "VSQX".
The difference between VSQ and midi is that midi only saves the basic notes, this allows it to be used with a multitude of music-related software and plug-in to apply to different things. Beyond the tune, it holds very little information which is why it serves no other purpose except this.
VSQ holds Vocaloid2 engine specific details. It is capable of recording which phonetics are being used, the Vocaloid that uses them and what againstments the user has made to the song.
VSQX goes one step better and also notes things like plug-in details which are only capable of being used with Vocaloid 3.