Here is a clip from the movie "Pits, Peaks and Passes" from 1966 in which Marston Morse explains some aspects of Morse theory. If we look at a function f(x,y) of two variables representing a shape of a pond, imagine the water level to be at height c. We can look at the region f(x,y) ≥ c, which is the part of the land above water. Now, when c increases, more and more of the land gets under water. Morse looks at the peaks (maxima), pits (minima) and passes (saddle points).