Thanks for reaching out!
So, if an event has a “finite possible outcomes”, we mean that we can count the distinct solutions.
This is usually very prominent when it comes to Poisson distributions, because in Poisson events we are counting the number of occurrences over a given interval (of time, distance, or w/e).
The easiest way to tell if we’re dealing with finite (discrete) or infinite (*continuous) outcomes is to take two outcomes and ask the following question, is the middle point between them also a possible outcome? If the answer is “No”, we’re dealing with discrete values, if the answer is “Yes”, we then take the middle point and the starting point and pose the same question.
If you do this with time or distance, you’ll always find yourself saying “yes” and moving to a smaller degree of measurement, which is why those are continuous. Since we can’t have an event happen one and a half many times, then Poisson events are discrete.
Hope this helps!