What does factory unlocked mean?

I was looking to buy an iphone from ebay globalbuy and costs of some iphone's r low having at&t or sprint or verizon(i'm guessing they r sim card brands) but some others have a higher price but it says that it is factory unlocked, what does it mean, while you r at it can you tell me what exactly is sprint, at&t etc

You can't use an iPhone made for an American carrier (AT&T, Sprint, Verizon) in India. Sprint and Verizon phones are not compatible (they are CDMA devices), and the AT&T model uses different cellular frequencies, so you won't get 3G or 4G services.

If you buy one unlocked, you need to make sure it will work with carriers in your country.