From http://thewallaceline.blogspot.com/2006/11/double-line-spacing-in-dissertations.html:
It is standard practice to require dissertations to be double-spaced. In the age of word processors, one wonders why this practice persists. This must surely be a legacy from the days when dissertations were typewritten and students were allowed to make corrections in situ rather than re-print. Word processors have eliminated that problem. Double-spacing might also be suitable for drafts which require annotation for editing, but final copies of dissertations are not used in this way and modern techniques such as commenting do this job.
How did this tradition get started? The ability to make corrections on the printed thesis in the days of typewriters sounds like a pretty good guess.