Come up with a real-world problem in which only the best solution will do. Then come up with one in which a solution that is “approximately” the best is good enough.

Taking the example of sorting…

Best sorting algorithm is required when we need to sort a huge amount of data as soon as possible. For example, Sorting blog posts by date or items in an online store by price.

“Approximately” best sorting algorithm will work when we need to sort a small amount of data and/or without any time constraint. For example, analyzing data of a medical survey to make a conclusion after few days. Or finding out the ranking in a competition where 5 people participated.