Simple stopwatch program with tkinter
Globals

Generally speaking it's not a good idea to use globals like this. It harms re-entrance. What if you want to support two stopwatches at once, either in one UI or as a web server? Having globals like this will prevent that.

It also harms testability. It is more difficult to test methods that rely on global state than it is to test methods that are self-contained, having state passed to them either in an object context (self) or as method parameters.

One way to get around this is make a class with attributes number_of_seconds and is_counting (which I find would be more intuitive than stop_counting).

Booleans

This block:

if stopCounting == False:
    numberOfSeconds += 1
    seconds.config(text=str(numberOfSeconds))
    seconds.after(1000, counting)
elif stopCounting == True:
    stopCounting = False
    numberOfSeconds = 0
    seconds.config(text=str(numberOfSeconds))


is more easily expressed as

if stopCounting:
    stopCounting = False
    numberOfSeconds = 0
    seconds.config(text=str(numberOfSeconds))
else:
    numberOfSeconds += 1
    seconds.config(text=str(numberOfSeconds))
    seconds.after(1000, counting)


Variable names

They should be lower_snake_case, i.e. start_button.