The mechanisms behind the lack of sunspots in the late 16 hundreds to the early 17 hundreds (the Maunder Minimum) is debated.
Among the effects on the Earth was colder weather for extended periods...
They are the smallest and largest values a function can take on in it's domain.
So if f(x) is a function, and the max value occurs at a point A, then f(A) is the max and similarly with the min.