Hemoglobin A1C (HbA1C) is glycosylated hemoglobin, meaning blood glucose (blood sugar) is high enough to keep sticking to hemoglobin, the protein in your red blood cells that carries oxygen. Glycosylated hemoglobin can't do its job very well so oxygenation can become compromised.
Testing HbA1C provides information on how high blood glucose levels have been over the past 2-3 months. The higher the HbA1c, the higher average blood glucose levels have been. Levels above optimal are associated with pre-diabetes and diabetes and should be investigated further.