Why are minterms so important?
The underlying goal of using minterms is to simplify the logic used to reach a defined output. This includes component logic as well as complex FPGA's. By 'simplify' the logic I mean that there could be at least 3 possible goals. One is to have the minimum number of gates as part of a logic or numeric operation, another is to insure a fixed time delay to avoid metastable states, such as gating a clock signal, and another use is to prevent race conditions where a logic tree must be completed before another chain of logic runs. In other words (simple example); output C needs input B to have the results of thread A completed or C is not valid. Minterms and maxterms branch out into integrals and other logical deductions such as AB!C = 110 base2 = 6 'base 10'. For more detail that covers more than I can write in a day, I found this article in Wikipedia.