In theory the Board's only job is to fire the CEO (and hire the next one) but if you've ever been to a board meeting they hardly are like that at all. They mainly are to align the company's "journey" with the "journey" of all the other companies the board members are involved with.
Discontinued website theyrule.net had a really cool visual web of board members of high profile companies [0]. Amazing how many board members of one company are board members of a handful of others. It's like there's a breed of person who is just "board member".
It’s called an interlocking directorate[1] and is why a lot of access to power and capital is class based and not meritocratic. It’s also part of why C level pay has skyrocketed as the members of the boards all happen to have C level positions and they all end up approving the pay increases of the people who get to vote on their pay increases
I once heard a joke that, in the right environment "If you know what you're doing and show a little enthusiasm, you'll wind up on 6 boards before you can turn around and realize what's happening".
It makes sense that certain types of people would wind up on a lot of boards very quickly.
The biggest issue the board seats have become status ornaments. People grab these board seats and most of them don't understand the company or product are shy of taking responsibilities. You would see two kinds of people who are on the board - first they are in some executive positions in other organization and are already very busy and the second category of people who grab these board positions for fame but don't want anything to do with it.
As a Delaware CEO, there is more than this. It depends on if the company is private or public. There is a duty of loyalty and a duty of care. Both of them have specific obligations, including hire/fire the CEO, sales, resourcing (e.g. financial plan approval), compliance, a neutral voice on comp and other stuff.