Can I use a different carrier with my iPhone 4s received from provider? I've got an iPhone 4s from a provider, but they gave it to me without a sim card. It worked but I am wondering if I could buy a sim card, put it in the slot and use the phone with a different carrier, like a prepaid one?
If you got your iPhone from a carrier, it is almost certainly locked to that carrier, so you can only use it with a SIM from that carrier. The carriers subsidize the cost of the phones, for the opportunity to make money selling you the data/phone plan.  This is why purchasing an iPhone from a carrier typically costs $0-$200 while an unlocked phone costs $600-$1000.

It can be possible to unlock iPhones.  An unlocked phone can be used with a SIM from any mobile carrier, including carriers from other countries.

Unlocking is completely independent of jail-breaking, which relates to modifying the software to accept non-Apple-approved apps.