Place to sit and do some light work.
And (maybe counter-intuitive to some), access to _small_ bits of food. When I travel, I rarely feel like having the kind of large, greasy meal you often get at airport restaurants. A small bowl of spicy soup, a piece of fresh fruit*, some veggies, an espresso or two, all in one place ... that can be worth a lot. Sure, I can get all that in the terminal, but it's a hassle.
It should be obvious that I'm writing this from a U.S. perspective. In countries with more developed infrastructure, many of these lounge benefits fall away.
[* Honestly, fresh fruit by itself almost makes whatever access price worth it. After a long flight, on a long layover, facing another flight, it's a small reminder that there's an outside to all these sterile spaces.]