In the final episode of Dexter we saw that Dexter took Debra from the hospital and throws her into the sea. So what was the reason that he did that?
What was the significance of the scene. Why did he kill Debra?
Because she wouldn't recover anyway:
After coming this close to catching the Brain Surgeon, Deb ultimately would never fully recover from the gunshot wound the tough-talking (and acting) detective suffered in the penultimate episode. While she comes through surgery, a blood clot would later prove to be the one obstacle Deb could not recover from as she wound up on a ventilator that would be the only thing keeping her body alive. Recognizing that a future in which his sister would never eat on her own, speak or have brain activity, Dexter unplugs the vent and professes his love for Deb. Those would be the final words -- and the ones he's strived to feel since the series premiere -- that Dexter would say to Deb before she flatlined.
Jennifer Carpenter explains why her character needed to die:
Why do you think Deb needed to die at the end of the series? You've been adamant about that for a long time.
When I've been saying that in the press, it's been for selfish reasons. Your readers deserve an element of truth when you're talking about something that they care enough to read about. I wanted them to see the truth; I did want her to die. But it was more about me. Deb deserves some peace. There was this setup when she and Quinn (Desmond Harrington) were finally able to set their sights on a love that existed, but I don't know what kind of peace she would have found there because Dexter always would have been in that place. She always would have been making sure she was piling enough dirt on the secrets that existed with Dexter. I'm not sure a happy ending was possible for her. This was her happy ending.
Looking at the scene when Dexter takes her off the ventilator to make sure she has a merciful death -- do you think that's what Deb would have wanted?
She would have wanted him to have the moment where he would have had to consider it, where he couldn't help himself but to get emotional about it. I have to believe, unfortunately, that Deb dies not knowing how Dexter feels about her. She doesn't have access to his feelings, which is all she ever wanted.
TVLINE | Was it always the plan for Deb to die?
Well, not from Year 1, but certainly two years ago when we mapped this out. Dexter [in the finale] is as close to being a human being as possible – he’s within a plane ride of achieving his happiness — but he hesitates that one moment. And Deb, who is the closest to him of anyone, [suffers].
TVLINE | Were there any other possible scenarios in which Dexter “kills” Deb, other than him taking her off life support?
That was always [planned]. In a completely fully-aware [moment] of love, at his most human, he does something that he’s had to do a million times: to take someone’s life. That’s the irony of that. There is a certain bravery because she’s living as a vegetable – I hope that if that ever happens to me I have a brother who loves me enough to take me off life support. But Dexter’s now aware enough as a human being that the guilt and the punishment of that will last a lifetime.
BCdotWEB's answer is very good and explains the reason, and gives out-of-universe answers, too.
Dexter: She's in a lot of pain.
Debra: Then I hope she goes fast.
Dexter: Not likely.
Debra: Just shoot me if I ever get like that.
Debra: Hell yes. I'd do the same for you. Pull the plug, put a pillow over your head, whatever. I'd never let you suffer.
When I rewatches the show I had the feeling that this was the first hint where the authors tought of Debra being killed by Dexter when she can't recover.