A pure public good is a good that is consumed collectively; it is both non-excludable and non-rivalrous. These two main characteristics mean that people can't be stopped from consuming the good, and that one person benefiting from its consumption doesn't stop others from also benefiting. An example of a pure public good would be street lighting as it has both characteristics. There are also quasi-public goods (or near-public goods) that share some, but not all, of the characteristics of a public good. They are often not pure public goods because they are rivalrous when the good is in high demand.
The free-rider problem occurs due to people benefiting from public goods, even if they haven’t paid for them. Therefore, the price mechanism doesn't work as consumers won't choose to pay if they can wait and let others pay for the good. This free-rider problem leads to complete market failure and there will be a missing market unless there is Government intervention.