We need to know how our memory operations are arranged in our programs, because if we make incorrect assumptions, our program could crash. It's also important because if we evaluate our algorithm with the wrong assumptions, we won't understand its performance properly.
We define memory consistency as the order in which memory operations appear to execute(loads and writes).
We consider a setup sequentially consistent if machine instructions are not reordered from the order they are specified in the program, and if all processors see the same order of memory.
It's feasible to implement this using a single processor machine. But we don't really want to, because it's restrictive and we lose the power of doing multiple reads sequentially, forcing us to do a bunch of slower memory operations.
The hardware does some cool optimizations that we need to understand if we're going to write a system that takes advantage of those optimizations. We also need to understand them because they can have scary effects on code running on multiple processors.