The interrogator will know things that can help determine whether the target is lying or not. If he confirms things you know but he doesn't know you know, you're probably on the right track. It's never like in the movies where they just ask, "Who's in charge?" and ratchet up the torture until the guy answers. That would have near zero intel value.
We also talk about torture as a binary. There is really a whole range from mild discomfort to extreme pain, injury and threat of death. There is a whole range of activities to debate whether they are torture. Is threat alone torture? Some have committed suicide while facing legal threats alone. Others shrug off mere threats as just talk -- demonstrative torture could make those threats real to some and thus work.
On the flip side, the consensus (30 years ago anyway) was that if you're captured, you're going to give up everything when faced with torture, so go ahead and do so, just try to hold on for 24 hours before you do.
One of the reasons that I semi-assume that torture works, is that there are security agencies that continue to use it. That also means they choose to use torture versus other means, although there, you could argue that they're doing it as a time/cost-saving measure, and that you could theoretically get similar results with more work. That's actually a pretty strong argument against my "I assume it works because it's used" argument.