The "Solution" check mark is used to mark a work log / email as the solution. The solution turns green and easily visible in the history log.
This log is retrieved into the receipt sent by the user when a case is set to «Solved».
If you do not have a worklog marked as a solution when you close the case, there is no text in the «Solution» field in the email that goes to user. Then you have to fill in something there before you send the email.