My understanding of a Health Savings Account is simply that it's untaxed dollars used for health care. What is the HSA you are referring to?
You are probably thinking of a Flexible Spending Account. With an FSA, you contribute money to a plan. It isn't taxed, and you use it for health care. If you don't use it in a given year, it's lost.
An HSA is a bit different. Many companies, including mine, offer an HSA based insurance plan. In it, the premiums are very low compared to traditional plans, and the deductibles are very high. For example, in our company, the premium for the "traditional" plan was around 250 per month, and there was a 1000 dollar deductibel. In the HSA, the premium was around 60 dollars per month, and there was a 3,000 dollar deductible. In other words, until you racked up 3,000 dollars in medical bills, the insurance company didn't pay one red cent.
Meanwhile, you get to open up an HSA. Money you put into it is tax deductible, and there's no tax if you spend it on medical expenses. Unlike an FSA, if you haven't spent it by the end of the year, you keep it, and can spend it in future years. As long as you evenually use it for health care, there's no tax.
The company was obviously pushing us to join the HSA plan, so I did the math as to which one would cost more depending on what sort of medical expenses, and the HSA was always cheaper for me. That puzzled me until I thought about it a bit more. Why would the company want me to take a plan that provides the same benefits to me, but at lower cost? The answer is that ever since I joined the HSA, I actually pay attention to how much I'm spending. Until I hit 3,000 bucks, which in most years, I don't, that's my money I'm spending. Now, when the doctor gives me a prescription for a test, I try to find a lab that will do the same test more cheaply, or I simply ask the doctor how much it costs and is it really necessary.
Basically, it replaces traditional insurance with catastrophic insurance, which, frankly makes a lot of sense.