If your cellphone is GSM based it has a SIM card (a smart card).
If your phone is "unlocked" any SIM card can be inserted (SIM card is basically a network provider's chip that enables the phone to communicate with the provider's network). So if you are in the DR you insert a GSM SIM card from a provider here and you can use the phone the same way as a local would.
When the phone is "unlocked", any provider's SIM card can be inserted. If it is locked, it is locked to the specific provider's SIM card and if you enter another provider's SIM card, you usuelaly get a message along "INCORRECT SIM".
You can usually unlock the phone by asking your provider to give you the unlock code. Eventually, it can be unlocked in any cell repair shop in the DR for a small fee (cell repair shops are plenty). Having your phone unlocked is advantageous because you will then be able to use it in any country that has GSM providers and byu local provider's SIM card and call for local rates.
These are the GSM operators in Canada (if you are customer of either one of them, your phone is GSM phone with SIM card, but please, double check with your cellphone provider).
ICE Wireless
Microcell-Fido
Rogers Wireless
You can activate GSM SIM card from Orange here in the DR for 10 dollars, including 3 dollars call credit.