What are some examples of services provided by an ecosystem that are considered to have non-market values?
Market value is a value that can be measured in price. The price is found when a thing is sold on the market. But some things are public goods and cannot be sold. This means that there is no way to assign a market value to them. These things can have non-market value.
With regard to ecosystems, most of the non-market value comes from the enjoyment that people get from a pristine ecosystem. There is no way to sell the enjoyment that can be derived from sitting on a clean beach or swimming in a clean ocean. There is no way to sell the enjoyment gained by a birdwatcher in a canoe sitting in the middle of a wetland and watching birds. These kinds of spiritual, recreational, aesthetic, and educational services cannot be valued on the market. However, they clearly do have non-market values because people will spend money (in travel costs, in buying the canoe, etc) to enjoy these services.