So everything has both a private cost and social cost. The private cost is the cost to those involved in a transaction, the social cost is the total cost, the private plus any external costs.

Likewise, there are private and social benefits, though for now let's assume no positive externalities so these are the same.

I'm going to assume you have a rudimentary understanding of economics. Like with supply-demand, we can find the equilibrium production amount for a product (widget) by looking at where its marginal cost equals its marginal benefit. That means the final widget made costs as much to make it as you benefit from it.

A private individual will maximize their widgets according to their private costs and benefit. But that means, because they aren't accounting for their true cost, they're going to produce what is best for them, but not for society. The socially optimum amount of widgets is when you maximize production according to the social costs. Likewise for social benefits.

However, if we, say, tax them according to the difference between the private cost and the social cost, then their private cost rises to equal the cost to society. Then, when they find their equilibrium, they'll get to the social optimum.

If you want, I can draw some graphs to help out.