To integrate is to make parts of something into a whole. It also means to become one unit, or to make a place (like a school) open to people of all races and ethnic groups.
One of the results of the Civil Rights Movement was the decision to integrate the schools of the American South. Before this point, African-American students went to different schools than white students. After the decision to integrate the schools, students of all races went to the same schools. Integrate also means to make into a whole or to incorporate into a larger structure: "If your school is missing a unit on thermodynamics, your science teacher could integrate it into the curriculum."