I have wondered that too. http://support.tixati.com/settings%20-%20transfers%20-%20local%20files
gives an answer:
Incomplete Piece Storage
This is where the software will store small fragments of downloaded pieces before they are complete. The data is stored separately because only complete pieces can be hash-checked for integrity, therefore it would be dangerous to save this data into the main downloaded file. This location should have at least 40-50 MB of free space available otherwise data may be lost between sessions.
I am having trouble though with understanding it takes up too much disk space. I have been using Tixati for several years and yet my folder for incompletes is under 8 MB total, hardly enough to be concerned about.