There are six values for status: New, Open, Pending, On-hold, Solved, Closed. A ticket's status can be set and updated either manually by an agent or automatically via your business rules. A ticket's status cannot be changed to Closed manually however; that is handled automatically via your business rules.
New means that the request was received but that it has not been opened and has not been assigned to an agent. The New status can indicate that the support team is evaluating it to determine who should be assigned to resolve it. After changing the status from New to another status, you can't change the status back to New.
Open means that the request has been assigned to an agent who is working to resolve it. Once a ticket status changes to Open, it can never return to New. If your tickets are being created in the Open status instead of New, see Why is my New ticket being created in Open status? in our Support Tech notes.
Pending means that the assigned agent has a follow-up question for the requester. The agent may need more information about the support issue. Requests that are set to Pending typically remain that way until the requester responds and provides the information the agent needs to continue resolving the request.
On-hold means that the support request is awaiting a resolution from a third party—someone who is not a member of your support staff and does not have an agent account. This status is optional and must be added (see Adding the On-hold ticket status to your Zendesk in the Administrator Guide)
Solved means that the agent has resolved the support issue. Solved tickets are closed, typically, a number of days after they have been set to Solved (the exact number of days depends on how an Administrator set this up). Until a ticket is closed, the requester can reopen the ticket. For example, the requester may not agree with the agent that the support issue is resolved and reply back to the ticket solved email notification.
Closed means that the ticket is complete and can't be reopened. Requesters however can create follow-up requests for closed requests.