HbA1c is a measure of blood sugar levels.
Here's how it works: some of the sugar in your bloodstream sticks to proteins in red blood cells (these proteins are called "hemoglobin").
Red blood cells have a lifespan of about 3 months (but are constantly renewing within the body). Thus, it's possible to determine your average blood sugar levels - from the past 3 months - by seeing how much sugar is "stuck" to a sample of your red blood cells.
Blood sugar levels tested as a single glucose measurement, like with home glucose monitoring, can vary significantly throughout the day based on many factors, including a recent meal or physical activity. So a better representation of average blood sugar levels is HbA1c.