Michael McGowan's answer is correct.
The HDHP is like conventional insurance -- it is not like a "health care plan" that we're all used to. I.e. you don't want to have it pay out -- if it pays out, something bad has happened to you. (Just like you hope to never make a claim on your homeowner's, disability, or AD&D insurance -- that means something bad happened to you.) There are minor exceptions -- some HDHPs may cover preventive care, immunizations, etc to some extent.
The bonus in the case of the HDHP is that you get to put money to cover the deductible into a tax deferred account. The HSA is effectively a self insurance fund with the HDHP as backup.
Here's a concrete example.
Say you have an HDHP with a $2500 deductible. The monthly premium is $500. You put $3000 into your HSA.
Scenario 1: You remain mostly healthy throughout the year. You have a single doctor's visit, the doctor's office submits a claim to your insurance. The insurance doesn't pay because you haven't met your deductible, and you get a bill for $150. You write the doctor a check for $150 out of your HSA.
Here, you've spent $6000 on your HDHP premiums, contributed $3000 to your HSA, and spent $150 of that on health care. At the end of the year, your HSA balance is $2850.
In the following year, assume you plan to contribute another $3000 to your HSA. You can increase your deductible on the HDHP to $5000 (since you'll have $6000 in your HSA to cover out of pocket costs) and your monthly premium might go down to $400.
Scenario 2: You are hospitalized for a week. The hospital submits a $15000 claim to your insurance. The insurance pays $12500 since your deductible is met after $2500. The hospital sends you a bill for $2500 for the balance. You write a check to the hospital out of your HSA.
Again, you've spent $6000 on your HDHP premiums and contributed $3000 to your HSA. At the end of the year, your HSA balance is $500.
Scenario 3: You are hospitalized for two days in December 2011, and then again for two days in January 2012. Your deductible reset on January 1, 2012. The hospital submits two claims to your insurance: one in 2011 for $5000 and one in 2012 for $5000. The insurance company pays $2500 on the first one and you get a bill for the other $2500. Same thing for the second one -- you've got to meet the deductible all over again. You write the hospital a check from your HSA to pay the first one. Then you've only got $500 left in your HSA. But you were planning to make another $3000 HSA contribution for 2012 anyway, so you make the contribution, write a $2500 check to pay the second bill, and you've now got a balance of $1000 in your HSA -- and since you've met the deductible for 2012 you should have no more out of pocket expenses. (Assuming your plan doesn't have copays.)
