Actually it can be a pretty big deal, especially if you are older and you've had diabetes for a while.
Hypoglycemia causes anxiety, tremors and sweating. In more severe cases, you can get confused, lose consciousness, have a seizure, or even die. Think about driving and having all that sneak up on you. Or if you're asleep and don't wake up.
It's actually not that uncommon. In medical training, we learn that if a patient is found confused or unresponsive, one of the first things to do is check their blood sugar, or just give them some sugar through an IV.
Considering the risk, the American Geriatrics Society says that for older adults, the benefit of tight glucose control might not be worth it if you're getting hypoglycemia. They suggest hemoglobin A1C goals of 7.0 to 7.5% if you are healthy and have a long life expectancy, 7.5 to 8.0% if your life expectancy is less than 10 years, and 8.0 to 9.0% if you have multiple medical problems and a shorter life expectancy.
You should discuss your exact goals with your doctor. But you should also know that tighter control of blood sugar is not necessarily better overall. It's another example of "more is not always better" in medicine.