What explains Wonder Woman's decision at the end of the movie?

Its not entirely clear why Diana chooses to stay in the outside world at the end, but I think there are two theories that seem to have the most support from the movie:

She Has No Choice

When she leaves the island with Trevor, her mother tells her

If you choose to leave, you may never return.

Now, there's two ways to interpret this. It could be simply her mother expressing worry that Diana may get killed, and never come back home. But given what we know (and Hippolyta knows) about Diana, it seems odd for her to be worried about that.

On the other hand, she may be telling Diana that if she chooses to leave the island, she can never return. There is absolutely no explanation why that would be true, unfortunately. Clearly, the island can be reached by normal means, and the Amazons are worried about more Germans arriving. Also, Hippolyta doesn't use this same objection to sending other Amazons out to fight, she only brings it up with Diana. But we know that Diana's situation is special, so it's not unreasonable to think special rules apply to her. For one thing, she's not really an Amazon, so perhaps there is something tying her to the island that will break when she leaves. Or, perhaps Hippolyta means that Diana would draw enemies (like Ares) back to the island with her, so she would have to stay away for everyone's good.

She Has A Mission

To me, the more likely explanation (and the one I think fits thematically with the movie) is that Diana found her true purpose, and it meant staying in the world.

During the bulk of the movie, Diana believed that her mission was to kill Ares and end war forever. She believed that this would return human kind to the pristine kind and peaceful nature it had before Ares corrupted them. Of course, that turned out not to be true, but by the end of the movie, Diana had found something else to believe in besides destiny.

She had seen how horrible people really were, Ares notwithstanding. But she had also seen how good they could be, if given the chance. And she had seen their capacity to love each other, and how powerful that is. She had decided that, despite her mother's protests, humans maybe did deserve her help after all.

So, she chose to stay in the outside world because she believes that to be her true purpose. She is one of the people who can genuinely make a difference in the world, and help make it better, and that's what she chooses to do.

On a side note: there was almost 100 years between Diana's appearances in the DCEU so far; we don't know that she never went back home. Perhaps we'll find out in a future movie that she does visit, but chooses to live in the outside world for personal reasons.

In addition to the possibilities that KutuluMike listed (She Has No Choice, She Has A Mission) there is the possibility that:

She Did Go Back

That is: it's possible she did in fact visit Themyscira in the time between the WW1 scenes and the modern scenes at the Lourve.

The movie clearly showed that she now lives in our world. But there is no evidence that she never went back to her home.

We simply don't yet know what happened in between those two timelines. Perhaps a future movie will fill it in.

If she did go back, you might wonder why that wasn't covered in this movie. It's possible a reunion scene was drafted but cut due to pacing. Once she kills Ares the movie has to come to an end quickly. There's a lot of character interaction to cover in a reunion and it'd be better served as an opening flashback in the sequel than as a blink-and-you-miss-it insert or campy-hug-montage at the end of this one. They also might not have decided yet whether Thymescira will appear in future movies. Maybe they aren't sure they can get those actors again.

The possibility that she went back is actually compatible with KutuluMike's 'She Has A Mission'concept. It's possible she went back, mourned her sisters killed in the beach fight, told her story, explained her mission to save the outside world, and left again. Another possibility is:

She Can't Find It

She was asleep from shortly after they left Themyscira until they had already arrived in London. Captain Trevor was awake but he's now dead. She can't get directions from him. She has no way to find the crew of the Tugboat that picked them up. Only Captain Trevor spoke to them. All the Germans died there. The best lead she has is the last known location of the German dreadnought, but it might have traveled quite far in pursuit of Cpt. Trevor since it last radioed its position back to German Command, and that information might have been lost.

So all she knows is it's in the ocean, not more than about 12 hours from London (because it'd be weird for here to sleep longer than that). That's a huge search radius. This is even assuming that going back to the same place will work. It's alternate dimension bubble might float around on the ocean currents! It could be anywhere if so. Maybe it is controlled by fate or magic, and can only be found when it wants to be. Finding her home could be the drive of a future movie.

Here's the deal, during the events of the war up until to the fight with Ares, she finally realized that Zeus made her for a reason, she was the godkiller, and man wasn't corrupt until Ares made him that way, so what happens is she decides to stay and try to remove that corruption in mankind due to Ares, also, I don't think he was the actual Ares, I think he was more of a manifestation of him....more like Loki or Dormammu from MCU!