Watch as two sprites obsess over random numbers.
Binary Search is a process used to sort and search for a specific thing. It divides the number of things you have to search for in half and (using sensors (in this case "higher" or "lower" indicator from the cat)) finds it imediately. Say you had a sea of red apples and you had to find an orange. Instead of picking up and looking at each and every apple in the collection, you can divide the number of apples in the collection in half and use some sort of orange-sensor to tell which half of the collection the orange is in. Much simpler than going through each and every article in the collection I'd say.