A carrier-unlocked phone can be used on another carrier by replacing the SIM card with one from a different carrier. You can buy carrier-unlocked phones if you pay the full price of the phone. Also, many countries now require carriers to unlock phones after 6 months, a year, or after the contract term is up.
Please note that, especially in the United States, phones on different carriers can use different frequency bands and so an unlocked phone may work poorly or not at all on another network. If you post what phone and carrier you have and where you might want to use it, we can help you.
Some online retailers can be rather shady. For instance my friend just bought an iPhone 5 model A1429 CDMA. Even though the seller advertises it as carrier unlocked, it's a Verizon model which means it will never work properly on LTE in Europe. That to me is deceptive sales practices.