Project manager and executive roles in determining project goals and scope
How much am I supposed to figure out what the project does, vs. just take what the executives give me and do it?
That depends on what you've been given. Typically, a project manager is appointed when a manager or executive has decided that something is worthy of moving forward as a real project. That implies the idea has been thought through by those executives (!). Thus you'd expect that they would express the overall business goals for the project, assumptions on what the project will create (its scope), and expectations such as due date and budget guidelines.
What can happen in the real world is one of the following:
You're given what is mentioned above—overall business goals and base expectations for schedule, costs, and scope. That's a good foundation for a project, but it's not all your team needs to know, so you'll have plenty to do to figure out what the project does in terms of how to go meet the goals laid out by the execs.
You're given very little info to start the project with. If you're lucky you've a least gotten a decent written statement of business goals. But maybe you've been given a much more vague statement of goals (or been assigned a project via a drive-by conversation in the halls!). In that case, much more will fall to you as project manager to make sure the goals and the scope are fleshed out quickly.
You're given a lot of information to start, in fact it appears that someone has basically tried to define and plan everything for the team. In that case, it might seem like you should just go ahead and execute the plan. Hey, we can just get going! The danger is that all that information got created in a vacuum, or perhaps without certain key groups involved, or without adequate customer input. What if that plan is missing something really critical? What if the very detailed scope you're given leaves out deliverables from some other functional group? What if a particular group of customers' needs aren't even being addressed?
In this situation, no matter how shiny and ready to go all that great info looks, it's the project manager's job to fully understand and sanity check the goals, scope, and plan information with the team. Who is the customer? What are the business goals? Who are the customers and other stakeholders and have they been consulted?
So the overall answer to the question is that both the executives and the project manager have a role in determining the project goals. Regardless of what you're provided by those executives, it is your responsibility to define the whole project—what gets delivered and the requirements for those deliverables—and develop the plan and team to make it happen. Take the time to understand what is required and why, and take ownership of what you and your team are being asked to do.