For those of us who don't live in the US version of a democracy, can someone explain to me why a given candidate winning only a few particular states will guarantee them the presidency? It seems like they're saying "Oh I know that these 20 states will vote for me, and those 20 states will vote for him, so the race is only for the remaining few undecided states." which from a foreign perspective seems an odd way of doing things.

FYI the system here is that you vote for your local member, who probably belongs to a given party. The party that has the most members voted in forms government and the party leader automatically becomes prime minister, assuming he won a seat (which they always do, they're given "safe" seats). We don't hold a separate election for the country's leader.