Let me try: First-to-invent vs. First-to-file deals with the specific case where two parties invent the same thing at roughly the same time and then file patents on it. The US was one of the few countries that was "first to invent". What that meant is, if you invent something, and then later somebody else invents the exact same thing independently, but the other party files the patent before you, you would still get the patent. As long as you had solid proof of the date of invention, invention of course.

So, if you invent something today and filed a patent next week, you could still get a patent over somebody else who independently thought of it and filed for a patent tomorrow, as long as you had proof. That's because you were the "first to invent".

Today, however, the other party would get the patent because they were "first to file", even if you have all the proof on the world showing you were first.

Seems unfair? It sort of is, so why the change? Because 1) it's what the rest of the world does, and 2) it happened so very infrequently and the hassle of resolving it was relatively so great, that the US optimized for the common case and got rid of it completely.

Note that prior art is entirely orthogonal to all this. It still applies to all patent applications as before. In this case, if prior art exists that pre-dates both parties' dates of invention / filing, both would end up without patents