Externalities are effects that are external to the marketplace’s supply and demand cycle. Let’s say you make steel and I buy it. The price of the steel is determined by how much it costs you to make it, how much profit you want, and how much I am willing to pay. There are third parties in the mix though: the people near the steel mill who have to breathe the sooty, rotten-egg-smelling air. Since they are not buying nor selling the steel, the marketplace ignores them; there is no way to put them in the equation of supply and demand. The health and environmental effects of steelmaking are a cost of production, but they are borne by someone other than the mill owners. They are external costs.
Externalities can be positive too. If you have beautiful flower garden that I can see from my window, that benefits me. If I walk past a historic building every day and appreciate the tile work, that sight may give me more pleasure than the coffee I’m drinking on the way, even though I may not even know who owns the building. The garden and the building have external benefits. The problem with external benefits is that they usually aren’t monetized. You make no money from the garden, but I will mourn if you pave it over. I pay for the coffee; I don’t pay for the beauty.