Diabetes isn't a yes and no thing. It's a continuum, where obviously at one end you don't have diabetes, and at the other end you obviously do, but for many people kind of in the middle, it's hard to categorically say. What your doctor means is that you have some of the changes that are associated with diabetes, but not enough to be definitely called diabetic.
The HbA1C is basically a measure of how much glucose is bound to haemoglobin. Because red cells have a lifespan of around 120 days, it's a good measure of how good your blood sugar control is over the last couple months - a lot better than the old glucose tests which used to measure differently depending on when you last ate.
If you're interested in changing your life, now is the perfect time - because much of the basic changes in diabetes is down to blood sugar and how your body controls it, and at this stage it's largely reversible. Eat healthier, exercise more, etc. If you get into later stages of diabetes, some of the nastier things become less reversible.