I haven't worked on campaigns for a LONG time but I don't think the basic answer has changed much. It's media and labor.

Presidential and statewide elections are a little different, but in most races the average voter isn't putting a lot of thought into an individual candidate. The bulk of that money isn't being spent to convince a voter to vote for an individual, it's convincing them to vote at all in full knowledge that most will break for one team or the other. It's part of why so much of the messaging is based at the lowest common denominator - it's more effective to spend money telling people that the "GOP hates women!" or "Dems want boys on your daughter's volleyball team!" in order to get the emotional response that will encourage action. Once you identify one of your "team", you basically spend money harassing them to vote until they do.

The groups that tend to spend more money win for the same reason that a product that is advertised more heavily, all other things being relatively equal, will outperform the product that advertises less.