First Timeline:



Wormhole opens. Mann and Brand and Cooper work on the Lazarus Project. Cooper flies on the final mission (the mission he'd been training for without knowing it) with Amelia, going through the same trials and sacrificing himself in Gargantua to let her escape to Edmund's world. Amelia institutes Plan B on Edmund's world. Those people go on to evolve into Humanity's future, with a stable Black Hole to guide their sciences. They evolve to work in the 5th dimension, and decide they want to save their ancestors. THEY find Cooper in Gargantua and create the tesseract for him. They initiate their original gravity burst to down Cooper's training flight for the original Lazarus mission. This leads Cooper to leave the program, marry someone, and have children. This change creates a second timeline, and creates Murph, key to their plan.



Second Timeline

This is what we see in the movie. THEY cannot interact with Murph, because she did not exist in their original timeline, so they use Cooper in the Tesseract to communicate with her, via love and gravity. His purpose here is two-fold: to guide himself back to Lazarus after THEY diverted him and to bring Murph into Lazarus, to fulfill the promise of Brand's Plan A. Cooper rejoins Lazarus just as before and re-aligns his second timeline with his first. Once in the tesseract again (or the same original time due to 5th dimension mechanics) he relays the TARS data to Murph and she makes Plan A a reality. Cooper Station lifts off, and begins it's slow trek towards the Wormhole.

Cooper is released from the tesseract, and recovered on Cooper Station just outside Saturn for a final reunion with Murph before she dies. He then leaves in a ship to rejoin Brand on Edmund's planet, knowing that she he there alone due to the time dilation involved in the final voyage across Gargantua causing Edmunds to be long dead of old age. Cooper and Brand create the second age of Humanity, those that will become THEY as they wait for the survivors of Earth to reach them in their slow gravity ship.