Unlocked Phones are typically phones operating on a GSM network. (In the US, AT&T & T-mobile are the major providers)
Not all unlocked phones will work over a particular cellular provider’s network. Most of the basic phones offered by phone manufacturers (Nokia, Motorola, Samsung, LG, etc) are only equipped with radio chips for the intended market. For example, North American handsets operate in the 850/1900mhz band while Euro/Asian handsets operate on the 900/1800mhz band. Either of these handsets are useless when the service is operated outside of the band.
The more expensive phones on the other hand, could be equipped with multiple bands, making it usable worldwide, and is commonly referred to as International phones (Tri-band or Quad-band).
Having an unlocked phone, you can purchase pre-paid SIM card in the localilty you are in and use a local number while at that location on that phone. As you travel, you are able to change mobile phone provider SIM card to be able to use a local number and cheaper rates compared to roaming with your home phone number’s SIM.