The Main Terms:

Coinsurance:   What the insured will split with the health insurance company, as a percentage, usually after the deductible.
Copayment: A cost sharing agreement where the insured will pay a small fee for a service (like a $25 docotrs visit or $10 generic drug refill)
Deductible - The amount of eligible expenses the insured must pay before the health insurance policy will make payments for service
HSA - An HSA is a lot like an IRA, except the money can be used without tax or penalty for medical costs before the account owner turns 65.  An HSA qualified policy is a high deductible plan where all eligible expenses, other than preventive care, are applied to the deductible first.
The idea is to save money in premium with the high deductible plan and use any money in the Health Savings Account to cover the expenses before the deductible.  Once the deductible and any coinsurance are reached, the insurance company will pay the eligible expenses.

See a full health insurance glossary on the Insurance Shoppers website.