That's a complicated question because the Flu is sort of a weird virus (properly a family of viruses).

Basically, everyone got it. Or, more accurately, enough people got it that the percentage of people who had been infected, recovered, and were now immune became high enough that that particular strain of the flu stopped spreading exponentially.

Most people are familiar now with the concept of the "basic reproduction number" (or R0) of an infectious disease, the average number of new infections that result from one existing infection (obviously this isn't universal, it's just an average). This number also ties in with the "effective reproduction number" (Reff) which is R0 modified by other factors such as vaccination programs, quarantine or track & trace protocols, use of masks, and, of course, modified by the fraction of the population that is still susceptible (which changes based on immunity acquired from vaccination or recovery from a previous infection). If, for example, a disease has an R0 of 3 then when 2/3 of the population become immune to the disease it will have an Reff of just 1 (it "tries" to infect 3 people, but 2 of them on average would be immune so it can only infect 1), and current active infections will plateau (and then fall after the fraction of the population with immunity increases above that critical threshold). This is a state known as "herd immunity", a term that has been massively misused and misunderstood over the last year (we'll get back to that).

The flu has a pretty low R0, and the 1918 H1N1 pandemic flu (aka "spanish influenza") probably had an R0 somewhere above 1.5 or so. After the 1918 flu infected roughly 1/3 of the entire world's population (killing off roughly 1-6% of the human population in the process) it mostly stopped spreading through epidemic scale outbreaks, because too much of the population had become immune. It did not, however, go away, that's not how natural "herd immunity" works, rather it became endemic, and was just one of the circulating flu viruses for quite some time. The same thing happened with the 2009 pandemic flu as well, though it had an even lower R0 (1.1 to 1.2) and infected a smaller percentage of the world's population (though likely a greater number of people, somewhere around 700 million to 1.4 billion). It was also much less deadly than the 1918 flu, likely causing under half a million deaths worldwide (a case fatality rate of well under a fraction of a tenth of a percent). That 2009 pandemic flu strain is still circulating, by the way, even today, and if you get a recent flu shot you will probably receive a vaccine for that strain (among others).

Herd immunity created through vaccination programs is designed to drive the population immunity levels significantly above the herd immunity threshold, causing epidemics to cease and with continued maintenance of vaccinations causing local (or in some cases global) elimination of the disease in the wild. These dynamics are possible because you can push the immune fraction of the population high enough such that Reff isn't just 1 it's consistently less than one, so any case importation results in eventual natural elimination like dropping a match into water.

These dynamics almost never work out the same way with naturally acquired immunity, however, for several reasons, and this is why talking about naturally acquired "herd immunity" is incredibly misleading. The reality is that with most naturally acquired immunity an infectious disease will spread until it starts to approach the herd immunity threshold, instead of runaway exponential growth it slowly bends to a plateau, naturally hitting that Reff = 1 point. But remember, this is the threshold at which cases remain stable, not where they die out. But, because the disease will be infecting people from a progressively smaller and smaller pool, the infection levels will tend to fall down. But it won't just get snuffed out the way it could in a population that has been vaccinated above the herd immunity threshold. The entire human race isn't just one giant well-mixed pool, it's a complicated series of intermeshed social networks. That heterogeneity is what allows endemic diseases to circulate as they pass around between different sub-populations.

There are a few important aspects here that come into play. One is that naturally acquired herd immunity never lasts, it is constantly decaying away. Partly this is due to population dynamics. Old people die and babies are born, this removes some of the people who had immunity while replacing them with new people who are susceptible (this is one of the reasons why so many infectious diseases circulate so prominently in children under 5, because that is the portion of the population where there are enough folks susceptible to the disease for it to do so). Additionally, individual immunity is not a binary all or nothing thing, it has a degree of strength and a probabilistic aspect to it, it also has multiple components to it which have different levels of longevity (weeks and months vs. years and decades). Most immunities wane over time to some degree, but they also wane substantially in the months after recovery, making it possible to become re-infected by a disease one has recovered from (or making one more vulnerable to a closely related disease).

Additionally, disease transmission sometimes has a seasonal component, which is especially true for the flu. What this can mean is that a flu that has an Reff of less than 1 during the summer, for example, could have an Reff of greater than 1 during the fall and winter. Partly due to changes in transmissibility (attack rate, etc.), partly due to waning immunity in individuals, and partly due to waning herd immunity levels due to population level changes (susceptible children under 5 attending schools, for example). These factors are what allows a disease that might once have circulated at a pandemic level to transition into a seasonal, endemic disease, which was true of the 1918 flu.

As I mentioned, the flu is a weird and special case. Measles, for example, has been circulating since before the 20th century, and we still have the same measles circulating today (as is true of herpes, chickenpox, rotavirus, cholera, etc.), whereas the 1918 flu strain is mostly gone. This is because there isn't just one flu, it's a whole population of strains. These strains are able to recombine their genes in something akin to sexual reproduction or hybridization (if different strains manage to infect the same host simultaneously), this is why there are things like "swine flu" or "avian flu" because those strains represent a combination of previously circulating flus from humans and animals that produce newly infectious strains in humans. This is also why even though we've conquered certain diseases like measles and polio (mostly) in the developed world and are working towards global eradication we're still struggling with flu eradication, because there is a constantly cycling series of new strains (though if everyone got the flu shot every year we'd be a lot closer). But, on the flip side, one of the other peculiarities of the flu is that even though being infected, recovering, and acquiring immunity to one flu strain won't necessarily give you immunity to a brand new strain, it can give you some immunity to other strains. And it's this which causes some flu strains to essentially die out in the wild, because they get out-competed by other strains, or because somehow the background level of effective immunity to that strain (from cross-immunity from other strains) becomes high enough to cause it to die out.

That's basically what happened to the 1918 H1N1 strain. It infected a third of the population of the Earth, then it went into the background as one of the circulating seasonal flus, and then it eventually just faded away through "chance" (basically, other circulating flu strains that maintained a level of immunity in the population against the 1918 strain that it eventually stopped circulating). That's a thing that can happen with flu strains but tends not to happen with most infectious diseases.

Edit: I want to make a note here about healthcare interventions related to the 1918 pandemic, something I've completely left out of the above. It's very difficult to estimate the degree to which such efforts (medical treatments of the sick, use of masks and isolation, etc.) were effective or how many lives they saved. Partly this is because we have so little good data from back then (particularly on the global level). It does seem that to some degree those efforts prevented the flu from infecting as many people as it could have, but this is just a guess based on squinting at the data. The complexities of flu strain dynamics run deep, and are much more complex than a single strain infectious disease, trying to figure out the exact details from a hundred years on is probably not possible at this point.