Out-of-pocket costs include expenses that your insurance company does not feel are covered services included in your plan. Some examples would be elective procedures, such as cosmetic surgery or procedures specifically excluded by your insurance company. If you don't want to have to pay for something out-of-pocket, you can easily find out what services are not covered by your insurance company by calling them and asking.
Another main out-of-pocket cost in health insurance are the costs you are expected to pay for covered procedures before your insurance will pay. The two primary ones are your deductible and co-insurance. The deductible is the amount you have to pay, out-of-pocket, before your insurance company will start paying.
The co-insurance amount is the percent you are required to pay towards a covered procedure. For example, your insurance company may cover 80% of your surgery and you have to pay the remaining 20% out-of-pocket. There is usually an out-of-pocket maximum and once that is reached the insurance company will cover 100% of the costs and the deductible and co-insurance payments count towards the out of pocket maximum.