They explained why they captured a Dalek. It appeared to be dead in space, so it seemed like a great opportunity to study the Daleks to help them fight the war against them. Then once they started taking it apart, they realized that it wasn't just a machine, but a living creature inside, so they stopped torturing it and it became a prisoner of war. They still had enough compassion left in them to let it live, since it was seemingly harmless at that point. Yet that didn't extend to the Doctor when they were going to kill him, so they were pretty conflicted with the whole war, I think. Fighting the Daleks was a necessity for survival. I think they used this story not only to explore the Doctor, but as a parallel too.
I think the Doctor's motivations were clear. The Doctor would want to do it out of pure curiosity regardless, but he was also conflicted about it, which is why the first thing he did was grab Clara. He didn't want to help a good Dalek, because he didn't believe there was such a thing. He asked Clara if he was a good man, and she wasn't sure, then she told him he was being prejudiced against the Daleks. Clara has become the Doctor's moral compass as he struggles with who he is. He needs her as his conscience.
There was the typical benevolent part of the Doctor that wanted to help another living being in need, one that had shown signs of change. If one Dalek can become good, it could influence the rest, and prove that nobody is beyond redemption, not even the Doctor's oldest nemesis. Maybe the Doctor had to prove this to himself too, that if they can be redeemed, so can he.
On the other hand, there's a cynical side to this Doctor that hates the Daleks so much that he doesn't believe there's such a thing as a good Dalek, because he's had 2000 years of his life telling him otherwise, and he wants to see why this one is good, and prove that it's a malfunction, and not a sign of growth.
I think this also ties into the idea of disliking soldiers that ran through the episode, because they fight the same internal battle constantly. The Doctor didn't want another soldier like himself on board, that could justify killing and hatred. The Doctor's dark side comes from fighting the Daleks in the time war, and fighting them on Trenzalore for hundreds of years. He needs Clara with him, the girl who wanted him to find another way to end the time war, and only wants to see the good in people, to help him be the good man he always aspires to be, The Doctor.
I thought that was all done well in this episode, but the show does move very fast, so even missing a line or two of dialogue can leave a hole in your understanding of why something is happening. But the more I think about it, the more all of the dialogue in the episode (and season) fits with these themes.