What is a ticket exactly?
A ticket is a support request.
As said it's a support request. A way to see it is when you call customer support (or write e-mail) regarding a problem, question, request for some service, adding/removing a service, etc, a ticket is created (this is not only Mt. Gox, but all large enough companies with enough volume of customer support).
When you call the first time, a ticket is created, and designated by a ticket number. As long as your problem is not solved, you exchange e-mail or call back, the support continue for that same ticket. Everything is logged and tracked, so when you call back, even if a different person answer, they can follow on your problem, previous problems you had, etc. When the problem is solved, the ticket is closed (still in the system, just the status is "closed"). That's the purpose of a ticketing system, to track support requests, categorize all the ticket according to different areas (complaints, support, questions, etc. About product #1, product #2, product #3, etc.).