A positive externality occurs when the production or consumption of a good or service generates a benefit for someone else who did not produce or consume the good.
Two neat examples of positive externalities are vaccination and education. I discuss these next.
Vaccination as a Positive Externality
I usually get the flu vaccine. In 2018, I even documented it for posterity, I took a photo and then tweeted about it, my caption “be the externality!” I was quite proud of myself that day.

I was proud and unhappy. The needle hurt my arm, which was sore for a few days. Ugh. But I didn’t want to get sick, so I did it and proceeded to post my bravado on social media.
Wait a minute, you say, the benefit of getting vaccinated seems to accrue only to you, you are not the one not getting sick! Where’s the benefit for others, you ask.
Thanks for pointing that out! Let’s talk about the benefit for others. In particular, let’s talk about something called “herd immunity”, or “community immunity”. Here’s the gist of it:
Germs can travel quickly through a community and make a lot of people sick. If enough people get sick, it can lead to an outbreak. But when enough people are vaccinated against a certain disease, the germs can’t travel as easily from person to person — and the entire community is less likely to get the disease.
US Department of Health and Human Services.
You may think of it like this:

So, the moment my getting vaccinated against the flu helps to prevent others from getting sick, or helps to prevent the spread of the disease, which clearly benefits others, that is when the externality occurs. You’re welcome, by the way!
Education as a Positive Externality
It will probably not come as a surprise if I tell you that education improves people’s job prospects (FYI, this is the possibility that something awesome will happen).
Indeed, the probability of being unemployed if you have a college education is usually about half that if you only finished high school. By the way, being unemployed means that you don’t have a job when you really want one and are actively looking for it, not just sitting on your couch lamenting to the stars that you wish you were working without giving said stars a bit of a hand in landing that job.
But wait, that’s not all! Did you know that college graduates earn nearly twice as much as workers with a high school degree? Kid you not! We’re only talking about roughly one $1 million over a lifetime of earnings, but who’s counting? Yes, you read right. One. Million. Dollars. Let that sink in for a bit.
The Bureau of Labor Statistics summarizes the two points above in one of my favorite charts:

More dough and less likelihood of being unemployed sound great, but this is only the private benefit, i.e. the benefit that accrues to the person getting the education. FYI, and for completeness, the spell of unemployment also tends so shrink with education, and that means the more educated you are the shorter the time span you’ll be unemployed.
What do others stand to gain, you ask. I’ll get to that now.
In 1955, Milton Friedman wrote the following about education:
A stable and democratic society is impossible without widespread acceptance of some common set of values and without a minimum degree of literacy and knowledge on the part of most citizens. Education contributes to both. In consequence, the gain from the education of a child accrues not only to the child or to his parents but to other members of the society; the education of my child contributes to other people’s welfare by promoting a stable and democratic society.
Friedman, Milton. “The Role of Government in Education.” In Economics and the Public Interest, edited by Robert A. Solo, 123-144. New Brunswick, New Jersey: Rutgers University Press, 1955.
It turns out, the benefits of someone getting an education extend beyond that person and actually contribute to improving others’ lives.
For starters, the more educated tend to vote more, and by that I mean that they register more to vote and actually show up! So, it is likely that the more educated the population, the better the democratic process and institutions tend to be. Naturally, the likelihood of one single voter making a difference is infinitesimally small but, on aggregate, voter ignorance, albeit rational, can lead to disastrous decisions.
The more educated also tend to stay away from criminal activity. For starters, the opportunity cost of crime is higher the more educated you are, as the higher potential earnings mean the more you stand to lose if you land yourself in the slammer. But this is only part of the story. The other part comes from the fact that in order to pursue an education people are busy and not pursuing a life of crime (ah, trade-offs…). This is called “dynamic incapacitation”, and it means that keeping young people in school at a point in time when crime rates tend to peak, at that is around 18 years of age, effectively keeps them out of trouble. Makes you appreciate compulsory school attendance laws, a tad more, doesn’t it?
The more educated also tend to live longer. Actually, not just longer, live, period. Did you know that the children of those with more education are more likely to survive? True story! Of course, you could tell me that those that are more educated also tend to be wealthier, thus better able to seek medical help and preventative care, but that is not all. Education also improves people’s cognitive abilities, and that allows them to make better choices throughout their lives, thus improving life expectancy.
The more educated also tend to have longer marriages. So, although marriage is the leading cause of divorce (ha-ha!), the likelihood of quicker end to the forever-do-us-part story decreases by almost half if the women have a college education. This would not be such a big deal if research did not show an interesting fact: married men tend to live longer than their single counterparts. And the results get better the more educated the wife, as men married to more educated women enjoy longer life spans than those married to less educated women. But hold on a moment, if you think that being married is good for health, look closely. I said “men”, not people. Indeed, at least for women, wedding rings should come with a health warning (I liked this sentence so much I stole it verbatim). It seems women do better than men when living alone, so it may be more important for men to be part of a marriage.
So, my whole point is that being vaccinated and being educated is both beneficial for the individual and beneficial for others. The last bit not being reflected in the value the individual who gets vaccinated pays for the vaccine or in the value the individual who gets an education pays for the education makes it a positive externality.
In The Real World
Of course, you could ask me whether the true price of vaccines or the true price of education in the real world reflect their externalitiousness (not a real word but it should be).
The answer is yes, that is precisely why both vaccination and education tend to be cheap through heavy subsidization. A lower price should stimulate purchase (through an increase in quantity demanded) without deterring production (through a decrease in quantity supplied).