a) this is a performance/compensation review meeting
b) this is a weekly/biweekly/whatever infinitely repeating meeting
I think most managers who ask for 1:1 meetings are talking about case (b). I do.
I don't schedule 1:1 meetings for local employees unless they ask; I do schedule 1:1 meetings for remote employees. My feeling (which I have mentioned to everyone) is that people I see most days have the opportunity to ask questions and bring up concerns any time they feel like it, but a person I can't bump into in the corridor deserves extra time for that.
My 1:1 agenda is loose: tell me if anything isn't going the way you want. Concerns about your work, other employees, the strategic direction of the company... this is an excellent time to bring it up. I can help with technical problems, or discuss the issue and refer you to the right person. Want to go to a conference? Want to tell me about the conference you want to? Anything vaguely company-related in on-topic, and I don't mind diverting off-topic much, because we'll have another meeting next week.