Jazz is a very big tent!
I could describe it as: Not a specific melody or style of melody, but a particular approach to melody. Not a specific rhythm but a particular approach to rhythm. Not a specific harmony but a particular approach to harmony. All of these "approaches" should have at least an acknowledgement of the tradition of jazz that has come before, even if the extent of that acknowledgement is "but I'm doing it my way." And all of these are optional. You can mix and match and still call it jazz.
(I may have accidentally described M-Base instead of jazz, which isn't what I was going for. Oh well.)
Possibly the only way to say for sure that something jazz is to find two people who agree that it is jazz, and then it's jazz.