Here are some ways it's used:
* Surprise: "Jeez, that was close!"
* Annoyance: "Jeez, why do I always forget my keys?"
* Disbelief: "Jeez, you're kidding, right?"
"Jeez" is considered informal and is often used in casual conversation. It's a common expression in English-speaking countries.
It's thought to be a shortened form of "Jesus" or "Jesus Christ," but it's not used in a religious way.