Integration occurs when separate people or things are brought together, like the integration of students from all of the district's elementary schools at the new middle school, or the integration of snowboarding on all ski slopes.
You may know the word differentiate, meaning "set apart." Integrate is its opposite. When you integrate things, you bring them together. So integration is the act of doing just that, like the integration of African-American students into mixed-race schools after segregation was outlawed in the 1950s, or the integration of computers in businesses that had previously only used paper-based record-keeping.