Skynet basically assimilates him at a cellular level. He is sort of human but has the mimetic alloy coating and healing his cells. He's kind of the "Vision" of the Terminator universe. It somehow merges with him though because it retains all of his human memories and even aspects of his personality. Pops says it is something that cannot be cured and Reese tests that out several times by pleading for John to "fight it" and whatnot to no avail. I was actually very happy that John couldn't fight it because they always seem to find a way in movies like this, lol.
At the beginning of the movie when the Resistance fighters capture the Time Displacement equipment it is explained to Reese that anything non-organic will overheat and explode, kind of like tinfoil covering a potato in a microwave. So he has to ditch his clothes which is no surprise to those of us familiar with the series. The movie ends with Cyberdyne counting down to the release of "Genisys" which is the trojan horse operating system that will connect over a billion users in the cloud with this new fancy Siri-like AI (but since it's really Skynet it's a male personification instead of female.) Genisys, and now time displacement technology, are now created by Dyson and is going to go "live" unless of course the heroes can stop it.
Pops, Sarah, and Reese go to Cyberdyne to blow it up, of course T-John is there waiting for them and they have this epic fight. One of my favorite moments in the film has Reese beating T-John's endoskeleton with a metal limb while he shouts "Now Sarah!" and she starts pumping it full of rounds with her super shotgun. It was a very awesome tribute to the final battle of Reese in T1 *AND* Sarah trying to take out the T1000 with her shotgun in T2 and it was really cool seeing both finales kind of fused together a bit.
But of course they can't kill T-John so Pops grabs him, turns on the prototype time machine, pulls John into it while Sarah is freaking out. T-John looks human be is still coated in metal at a cellular level so he's vulnerable to the machine. Sarah pleads with Pops to get out of the machine because he's so BD he also has lots of metal exposed, Pops says one last line that really did make me tear up a bit and he sacrifices himself to obliterate the screaming T-John in the time displacement field.
Reese and Sarah have the obligatory escape out of the exploding building scene where Genisys is stopped from going live due to the explosion of the time field.
There's a last spoiler or two that I'll still not share but it has to do with leaving the movie open for a sequel. Even though this is the first of a supposed trilogy it really had a satisfying finale since they really did kill T-John. Which really made for an awkward dilemma for Reese and Sarah. They pretty much determined that they can never have sex since they don't want to create evil John but the movie ends with the assumption that they'll probably still hook up since they think Skynet is destroyed and that they're all "safe."
Wow, you saw the very moment where a little piece of him died inside 
