The fall is the American way to say [autumn][1], which is one of the four seasons of the year that comes after summer and ends before winter. You might now ask why is there no definite article in front of *fall* in *by fall*. Well, it's often the case in English that articles are omitted when they follow the preposition *by* when it is used to indicate a deadline or the end of a particular time period. I think that's why the definite article is missing there.

So, what public health officials are trying to say is that by the time it's autumn, we're going to have a resurgence in the number of covid-19 cases, meaning, the curve that represents the number of people who have contracted the virus is going to go up again.

  [1]: https://en.wikipedia.org/wiki/Autumn