It's a good indicator of average blood glucose over time, as opposed to a one-time BG test.
Your blood cells live for a few months. The higher your blood sugar is on a regular basis, the more the glucose tends to get stuck to your red blood cells. That's what the A1C is measuring. The reason it's bad is that it's those glycosylated red blood cells that cause the tissue damaged associated with T2D complications: your eyes, your extremities (peripheral neuropathy), your kidneys, your brain...
In an average healthy person, A1C is at about 5%. That probably includes most people eating low-carb. That's where mine is. Some VLCers, carnivores and IFers get it more around 4%. If you're developing T2 diabetes, it starts creeping higher and higher. I think the diabetic range is considered 6+, though it might depend on the lab reference range, what country you're in, your doctor's opinion, etc.
I think A1C is also higher if you think you're perfectly fine treating your T2D with insulin, but you're still eating the SAD and on a chronic BG roller coaster. IMO, this is why so many clinicians are angry about the standard treatments for diabetics: the "just keep eating crap, cover it with insulin and you're fine" theory. It doesn't prevent the damage.
...at least that's how I understand it.