What's the difference between buying an iPhone through a carrier (At&t, virgin mobile, etc.) or Apple?

And why are they sometimes cheaper when you buy it through the carrier? Like, why are iPhones so much cheaper through Virgin Mobile than through other carriers? Is there a difference in quality?

Because they practically have you pay throughout the year(s) for the phone. If you buy it straight from Apple, it'll more than likely be unlocked and work on any carrier you choose and not just one. For example, if you buy it on Verizon or Sprint, you might have a slight problem getting it to work with AT&T and T-Mobile due to them using GSM

If you buy from a carrier, you're basically stuck with that carrier. Verizon uses CDMA and AT&T uses GSM so you can't just take the Verizon SIM card out and put in the AT&T SIM card and expect the phone to work.

If you buy from Apple and get the sim free version, it's pretty much a universal phone. You can stick in any SIM card and expect it to work. Comes in handy when you visit other countries.

The carriers spread the price of the phone over the course of 24 months, vs Apple where you could buy the phone unlocked at 1-time payment of the full price.

Its the same phone anyway you put it.