How to measure the “Heavy use” of OSM as per OSM policy

The page that you link to says "heavy use" twice. One is in this sentence:

Heavy use of OSM tiles adversely affects people’s ability to edit the map, and is an abuse of the individual donations and sponsorship which provide hardware and bandwidth

and another is here:

Heavy use (e.g. distributing an app that uses tiles from openstreetmap.org) is forbidden without prior permission from the Operations Working Group. See below for alternatives.

Presumably it's the second one that you're referring to. The "e.g." part explains the sort of thing that might cause a problem - you distribute an app and encourage people to use it, so lots of people who you have no control of might download your app and try and download lots of data (until they are all blocked). For completeness, further down it also says:

Bulk downloading is strongly discouraged. Do not download tiles unnecessarily.

Can you explain what you are planning to do, and also perhaps why you are planning to use OSM's tile servers rather than creating your own?

(edit)

After reading another question of yours it would appear that "distributing an app that uses tiles from openstreetmap.org" is exactly what you are planning to do. Don't do that - you'll get blocked. Create your own tiles and use those instead.