Let's get the scientific stuff explained and out of the way.
Hemoglobin is a protein that is found within red blood cells that carry oxygen
around the body.  The sugar in your blood that powers your body is called
glucose.  When glucose in your blood combines with hemoglobin it is now called
hemoglobin A1c (other names are glycosylated hemoglobin or glycosylated
hemoglobin). The higher the concentration of glucose you have, the higher
resulting concentration of hemoglobin A1c.  Healthy, non diabetic adults will
have a hemoglobin A1c concentration of less than 6%.  Unlike your blood sugar
concentration which changes constantly (for example with diet and stress) the
concentration of hemoglobin A1c changes slowly, increasing when your blood
sugar level is high.  The reason why hemoglobin A1c does not fluctuate
like blood sugar is that glucose cannot be removed once it is bound to
hemoglobin and can only be removed when the red blood cell is
replaced by the body every 90 - 120 days.  This is why hemoglobin A1c
reflects the average glucose level within your body for the past 6 to 8 weeks.  
Your Hemoglobin A1c test result is your body's glucose report card for the past 8
weeks which takes into account your good and bad days.  The American
Diabetes Association (ADA) says "it's like getting your blood's batting average."
Knowing your hemoglobin A1c?
Being informed and educated about diabetes is the most important thing a
person living with diabetes can do for themselves.  There is good evidence that
controlling glucose levels reduces the incidences of complications with
diabetes.  A single point reduction in hemoglobin A1c can reduce the
risks of cardiovascular accidents by about 30 to 35 percent.  The
Diabetes Control and Complications Trial conducted by the National Institute of
Diabetes and Digestive and Kidney Disease (NIDDK) demonstrated equally
substantial reductions in risk of eye, kidney, and nerve disease with lower blood
glucose levels.
Molecular structure of hemoglobin that
glucose glycosylates or "bonds"  to.  The
higher your glucose levels the more glucose
that gets attached to hemoglobin.