A Fermi problem is an estimation problem, where the objective is to answer a question that requires a number of assumptions be made, and for which the final answer can usually be best given as a range of possible values.
Some examples of Fermi problems are:
Could the forests of North America serve as the lungs of the world?
How many phone books are delivered in NYC?
How many piano tuners are there in the United States?
How many different civilizations like ours exist in our galaxy?
An activity that students could do would be to brainstorm their own Fermi problems, and then choose one of the problems to attempt to solve in a small group.