What is it about pure public goods that means that the market will not adequately provide those goods?

Pubic goods have two characteristics: they are non-excludable and non-rivalrious. Being non-excludable is what causes them to not be adequately covered by the market. If you can't stop people from using your good/service for free, then you will not have as great an incentive to produce such goods/services. An example is a firework show. Assume I am thinking of creating a firework show and charging people who come to my small plot of land to see it. Many people will just stand outside my plot of land and get most of the utility of watching for free and thus I don't get any money for giving them the benefit. Thus, I will be less inclined to host a firework show.