Things or people that are integrated have been brought together, so that they live or work together. They're no longer apart or segregated.
When something is integrated, it's united — different things are now together, especially things that used to be apart. Schools haven't always been integrated in this country. At one point, kids were assigned to different schools based on their race, until education became integrated. Computer programs are integrated when they work together well with other programs. If a doctor and pharmacist have access to the same files, then their records are integrated. Integrated things are together.