It doesn't sound serious, but it never hurts to understand what it is.
With Denard Span's move to the disabled list, retroactive to June 10, the organization's stand is that they're taking a precautionary measure. Doctors have said that Span could be available for this weekend's series in Minnesota against the Houston Astros, but the Twins want to give him (via Ron Gardenhire) "the extra few days".
Vestibular Neuronitis, caused by a viral infection of a nerve that connects to the brain stem, comes on suddenly and has one primary symptom: vertigo. Not the Jimmy Stewart crazy kind, just the "spinning room" kind that can make you dizzy. Basically, the vestibular nerve swells and tells the brain that you're moving, but your eyes insist you aren't, making you lose balance. There are side effects, like nausea and vomiting, but never hearing loss, and in most cases takes less than two weeks to dissipate. In rare cases it has lasted months.
In most cases, treatment is simply rest. It usually will go away on its own. Doctors could advise you to stay in bed for a few days, or give you a few balance exercises, but even severe symptoms can be treated with simple antihistamines (Benadryl).
None of the websites I've searched have implied that this is a serious condition in any way, and all have given the impression that only in the rarest of circumstances does the condition last more than two weeks. That's good news for the Twins, and even more importantly it's good news for Span.
Good luck, Denard. We hope you're back soon.