What are they? That's easy. They're (usually) regularly scheduled 2 person meetings with a manager and direct report. What are they good for? More fundamentally, who are they for? Once you know and internalize the last question answers to any other questions become much clearer, so let's tackle that part first and be very clear.
1:1 meetings, whether between a manager and direct report, a skip level, or a meeting with the CEO, belong to, and are for, the subordinate. Not the manager. Not the Director. Not the CEO. That's not to say those people don't get value, but the 1:1 meeting belongs to, and is for, the subordinate.
What are your 1:1 meetings good for? As much as I don't like design by counter-example (there's a topic for the future), 1:1 meetings are NOT status meetings. Status may come up in the course of a discussion, but that's not why you're there. That said, they can be about anything you want, because it's your meeting. Things that they're commonly used for are giving and getting feedback, understanding what your manager really values, identifying blockers and enlisting help, finding and taking advantage of opportunities, bringing up new ideas and issues, and career development. A corollary to owning the 1:1 meeting is that you also own the growth of your career. Your manager is there to help you and help you take advantage opportunities, but the responsibility is yours.
So take ownership of your 1:1 meetings. Make sure they're scheduled. I find weekly is best because if you miss one it's only a week. If you have them scheduled every other week and miss one suddenly they're monthly meetings and that's probably not frequent enough. Be flexible, but don't let you manager slide every time. Be willing to move an instance, but have it. Have an agenda, and share it with your manager early so they're prepared. Keep a documented record of the meetings, including notes and action items.