The HbA1c test is important for all of the reasons given above, but the rationale for testing - particularly the relatively infrequent testing - can be confusing. Also, there are a few wrinkles in interpreting the results of this test, of which you should be aware.
Haemaglobin (Hb), or Hemaglobin (Hgb) if you are American, is the stuff that makes blood red. It is a molecule that is found in "red blood cells", and it conveys oxygen from your lungs to the rest of your body. There are several variants of Haemaglobin - by far the most common and important is "Haemaglobin alpha 1" (HbA1). When Haemaglobin is exposed to glucose it occasionally binds to it in a chemical process called glycosylation to form a substance called "glycosylated haemaglobin" (which for HbA1 is called HbA1c). Since everyone's blood contains glucose, everyone has some HbA1c, but since diabetics blood is likely to contain more glucose than non-diabetics (unless the diabetes is very well controlled) then they are likely to have more HbA1c. The test simply measures the percentage of red blood cells that contain HbA1c.
The levels of glucose in the blood are always going up and down, and all that a Blood Glucose test will give you is a snap shot at a particular moment in time. Because the glycosylation process only occurs gradually the HbA1c levels don't change on a day to day basis. Therefore there is no point in doing the test very frequently. Red blood cells live for 3-4 months, they then die and are continually being replaced. For this reason, the HbA1c gives you a fairly good estimate of your average glucose levels over the previous few months. Typically, monitoring it once every 3 months will give you a good estimate of how effectively the diabetes is under control. An uncontrolled diabetic may well have an HbA1c of over 15%. You should probably aim for an HbA1c well under 6%, and some people manage to get it a fair bit lower. A non-diabetic has an HbA1c of about 5%, and the closer you can get to that the better.
Although HbA1c tends to be most doctors favourite means of monitoring long term diabetes control, it does have some drawbacks. Under some circumstances (usually in people with the very early stages of diabetes) it is possible for blood glucose to fluctuate such that it is too high and too low for equal amounts of time - which can cause the average (and hence the HbA1c) to be normal, even though blood sugars are swinging up and down in a potentially damaging way. Another problem is that some dietary supplements (such as large doses of vitamin C) and some illnesses can cause misleadingly low HbA1c readings.
That said, one of the main reasons that doctors give the HbA1c test so much credence is that it has proved to be a very good indicator of diabetic complications. The higher your HbA1c figures are, the more likely that you will suffer some of the more horrible consequences of diabetes.
In short, do your best to keep it low - certainly worry if it is above about 7%. However, don't get complacent just because you have a low HbA1c - it is still good practice to regularly test blood glucose, just to make sure that something else isn't giving you misleading HbA1c results.