With R2-D2 being a prominent part of both the Star Wars original and prequel trilogies, fans were excited to see his return in Star Wars: The Force Awakens. Yet the old droid was absent for almost the entire movie, as he sat in low power mode at the Resistance headquarters. While C-3PO hints that R2 is just upset with the loss of Luke, it appears as if there's more going on, especially considering how much R2 had gone through already. And while it was never explained during the sequels, an official explanation has been given.
As BB-8 arrives at the Resistance base, he holds a small incomplete map to Luke Skywalker and brings it to R2. The domed droid sits as an empty shell, with C-3PO saying, "You're wasting your time. It's very doubtful R2 would have the rest of the map in his backup data." Ironically, R2 does indeed contain the map, but with no one knowing this, they simply believe that "R2-D2 has been in low power mode ever since master Luke went away. Sadly, he may never be his old self again."
Already this raises questions and even suggests that droids are capable of feeling depressed. However, during Star Wars: Revenge of the Sith, R2-D2 witnessed his old master Anakin turn to the dark side and even attack Obi-Wan and Padmé. Yet he still seems in high spirits by the end of the movie, so shutting down because Luke is missing seems like an extreme reaction, especially since R2 is the type who would hunt down Luke all on his own if he had to.
Pushing away from the sadness idea further, R2-D2 just so happens to power on at the end of The Force Awakens, just as Leia has lost her husband. Upon the movie's release, fans theorized that R2 was powered on by Luke, as it was finally time for his location to be revealed. Yet that clearly wasn't the case, as Star Wars: The Last Jedi showed that Luke was adamant about staying alone on the island.
The coincidence between R2's awakening and the map is never brought up again. However, Star Wars: The Force Awakens: The Visual Dictionary explains: "As R2-D2 recuperates in his self-imposed low power mode, his diagnostic systems are attempting to organize the vast trove of information in his databanks from over seven decades of uninterrupted operation. The defragmenting of millions of exanodes within his memory is causing R2-D2 to "dream" many of his greatest adventures."
So much like a real-life hard drive, R2 was supposedly defragmenting and cleaning up his memory. Typically, droids have their memories wiped after a few years, but throughout the entire Star Wars saga, R2 kept all of his. This meant he had so much storage that simply organizing it all took years, and he finally got around to it after Luke had left.
While this doesn't explain why R2 happened to turn on at the end of The Force Awakens to provide the map, it still provides a better idea for his stasis. It's possible that his return was simply impeccable timing, or perhaps he could still hear BB-8 when he was in low power and realized that the Resistance needed his help. Either way, it was a great moment to see R2 return. And his reunion with Luke in The Last Jedi provides one of the most wholesome moments in the movie.