Wikipedia:
[...]Tickets are commonly created in a help desk or call center environment. Typically the ticket will have a unique reference number, also known as a case, issue or call log number which is used to allow the user or support staff to quickly locate, add to or communicate the status of the users issue or request.
These tickets are so called because of their origin as small cards within a typical wall mounted work planning system when this kind of support started, operators or staff receiving a call or query from a user would fill out a small card with the users details and a brief summary of their request and place it into a position (usually the last) in a column of pending slots for an appropriate engineer, so determining the staff member who would deal with the query and the priority of the request.