It is the time of the year during which it is acceptable to wear flannel (ex. - don't wear white after Labor Day). Flannel Season begins October 16th and runs through March 16th (the day before St. Patty's Day). However, this rule can be overridden if it is below 50F during the time that the flannel will be worn.
I can't wait for fall to get here because then flannel season will be right around the corner.