The term Israelites is used in different ways. Perhaps the most common is to refer to Jacob and his descendants. (Jacob is also known as Israel.)
Sometimes the term Hebrews or Hebrew race is used to refer to the descendants, including modern day Jews, but these terms are used more often by Gentile racists than by Jews.
The civilization of the ancient Israelites gradually came to develop in about 1800 B.C.E., and thrived until it came to an end in 70 C.E. Though the people who would become the Jews first lived in the land of Mesopotamia, they moved to Canaan, modern-day Israel, in about 1950 B.C.E.
The term Israeli is used for modern citizens of the State of Israel, regardless of race, ethnicity, religion, etc.