Why are the hottest and coldest places on earth over land, not over water?

Because the heat capacity of water is very high, meaning that it can absorb a big amount of energy (heat) while its temperature increases less than what it does in other bodies that have lower heat capacities.

In terms of equations:

Q α Cp * ΔT = > ΔT is inversely related to Cp = > if Cp is higher ΔT is lower.