The confusion is usually because a Dr or practise nurse has described the HbA1c as an 'average' of blood glucose over the last 3 months. Which it sort of is in a way, but actually is completely different.
The thing about fingerstick BG meter readings is that they only measure your (plasma calibrated) blood glucose reading at that moment. If you checked an hour or two later it would almost certainly be different. And if you check last thing at night and then first thing in the morning neither of those readings can actually reliably tell you what happened in between. You'd have to get up and check overnight if you wanted to know that. Or wear a continuous glucose monitor - but that's a different story.
This is how I think it works...
What is HbA1c?
It is a marker of how much glucose has stuck to red blood cells in your blood stream. Red blood cells (haemoglobin) go swishing about your body and as they travel the fluid they are swimming in has a level of glucose in it. Some of that red blood cells get changed by the glucose which sticks to them (they become 'glycated'). And the more glucose you have in your blood stream the more cells are affected. Once cells are glycated they can't change back, so they potter about for the rest of their 120 day lifetime until they get recycled. But importantly the higher your blood glucose, the more haemoglobin gets changed.
What some clever boffin realised, was that by measuring the proportion of the red blood cells that have got glucose stuck to them you had a sort of proxy marker for how full of glucose the blood had been over the last 120 days. And it was a marker that wasn't changed moment-by-moment as the blood glucose altered, it was more stable because of the lifetime of the red blood cells.
Not only that, you could measure it and then track likelihood of complications. And in general terms, the higher the HbA1c, the more likely a person was to have diabetes nasties come knocking at their door.
The weakness of HbA1c is that it can only give a general picture. It cannot tell you how stable blood glucose has been (whether there have been wild swings from high to low levels) and it can't give any detail about when high blood glucose occurred.
That's why many people on the forum are interested in it as a value, but rely more on fingerstick BGs to help them modify their diet, doses and activities to improve BGs day-to-day.