When you change the rules of transfer in a subset of nodes/users, then all of a sudden there is disagreement about who owns what: there are two ledgers, and you look at the one whose opinion about "ownership" you agree with.
So the "fork" is a fork in ownership or truth: a difference of opinion about who owns what. Nothing more, nothing less.
But it's a complicated economic effect to predict, because it's likely that the losing side (the opinion with the smaller number of nodes supporting it) will wither and die - one major value proposition of bitcoin is that it's universal. But what happens to the people who used that losing fork in the interim? Well, basically none of their transactions were "real" (they didn't take place on the ledger that eventually won), and if you sold something to someone on that ledger, then they have the goods/services, and you have nothing.