I like to think of it more or less as one big-ass circuit that connects everything, like a huge river with a bunch of streams that feed into it and out of it. Unlike natural rivers, though, the electricity basically “cycles” in one big loop, around and around, and equalizes as it goes… (as @Tride was explaining). Maybe it’s more like a closed-loop lazy river at a fancy resort/water park, in that it just goes round and round in a big circle. You can take a drink from it, or pee into it, but it’s the same body of water that will circle around and around. It’s an ongoing circuit, not a one-way trip.
When you “use” power, you take it out of that river (and ultimately turn it into heat that “evaporates” into the air), but any unused power, or power that you generate, just flows back into that big network to be consumed by someone else… might be your next-door neighbor, might be the utility, might be nobody. You can’t really measure “your” individual electrons; they just become part of that great river.
It’s a tortured analogy and the actual electromagnetic physics and technologies involved are super complicated, but mostly don’t matter for a homeowner. The payments you get are just a matter of mathing it out via meters that monitor your usage and production, plus/minus any incentives or disincentives (many states/regions have too much solar now and have to actually disincentivize it so it doesn’t destabilize the grid, like having a million people all peeing into the lazy river exactly at 3:04pm…)
Also, I don’t know if you already signed a contract, but if not, can I strongly recommend that you get 2-3 quotes from different area dealers?
I used to work in this industry (in manufacturing, retail, and installation) and the overall installed prices can vary dramatically between companies or even individual salespeople. A lot of the stuff is imported foreign commodity goods heavily subsidized by Chinese government price dumps, especially the solar modules themselves (what we call the “panels”), so many dealers have to rely on predatory pricing schemes or wily salespeople to make a profit. It’s entirely possible to get ripped off by a factor of like 1.5x-2x or more if you’re going into this blindly. If they offer a lease, be especially wary — it’s usually better to buy these days (separately financing through a bank if you need to).
Don’t just go with the first nice company you talk to, research customer experiences in your particular area and what the median price per watt should be. And don’t buy into long-term warranties; many of these small-scale regional solar companies won’t survive long enough to outlast the modules and inverters. It’s an incredibly cutthroat and volatile industry with installers and manufacturers dying all the time.
Edit: Also, never trust your dealer’s production or payback estimates. Do your own math — there are online calculators available, like Google’s Sunroof for an easy to use one or the government-run PVWatts calculator for a detailed one — to ballpark it. Many dealers are dishonest about this and you will often end up getting less than what they estimated and they will blame it on weather or whatever when in reality they were just overestimating on purpose.