If you're looking for a serious response, here it is! Guys, like me, would take an older car and race it with friends. If we were beaten, we would look to do modifications to our engines to make them faster. Common modifications were increasing the size of the bore (where the pistons are) and increasing the power stroke of the engine by increasing the length of the connecting rods to the pistons. These engine modifications were made using larger pistons and a longer stroke ("bore and stroke an engine") and would typically run at higher heat ranges and, thus, have "hot rods" as a result.
I have little knowledge about how the term was expanded to include most modified cars, but it was!!