In United States law, the concept of a "public figure" is used to determine if and when defamation or invasion of privacy have occurred, and in some cases whether someone's (or some other entity's) First Amendment or press-freedom rights have been violated.
The Supreme Court case that originally introduced this concept into law was the New York Times Co. v. Sullivan in 1964, a court decision that, among other things, held that public officials (or people running to become public officials) have to meet a higher standard of proof when claiming defamation because of their status as a public figure.
Sullivan was a police commissioner in Montgomery, Alabama who sued the New York Times for running a full-page ad purchased by supporters of Martin Luther King, Jr, which contained inaccuracies about how civil rights protestors were treated by the police in Montgomery.
The judge in the case ruled that the inaccurate claims in the ad were defamatory and awarded Sullivan $500,000 in damages, but the NYT appealed, having the initial ruling affirmed by the Alabama state Supreme Court, but then having it overruled on First Amendment grounds (in a 9-0 decision) by the US Supreme Court.
The general idea was that there was no actual malice—which is a legal standard that means, basically, the NYT didn't intentionally seek to harm the reputation of Sullivan—and thus, the ad was not (in the eyes of the court, at least) libelous.
This higher standard for proof when it comes to public figures was implemented to protect the press against lawsuits from people who are upset that journalists report upon them in a way they don't like, and who have the resources or connections to tie them up in court, potentially threatening their financial health as a consequence.
Allowing that to happen—as it has many times across US history (where lawsuits tend to be how we settle these sorts of things)—would have the de facto effect of killing-off the free press, as journalists would be incentivized to avoid reporting on powerful, wealthy people (and businesses), because if they said something such people didn't like, they could be sued out of existence.
This legal concept has become fuzzier and more pervasive in recent decades, as the internet and social media have pushed more people to the forefront, which in turn has put more sorts of people, not just business leaders and politicians (and corporations and political organizations), in the legally recognized limelight.
According to the Supreme Court ruling in Gertz v. Robert Welch, Inc—a case in which the delineations of defamation standards for individuals were further clarified to say, in essence, there can be no strict liability for defamation in the US, so there must always be some kind of negligence or a high level of intended criminality in order to prove defamation—a "limited purpose public figure" is someone who has either been pushed into the spotlight by circumstance, or who has put themselves there, intentionally, in order to profit or influence some kind of legal outcome or public conversation.
Talking heads who promote their industries on TV and online, then, but also folks who become spokespeople for a particular policy, might fall into this category of limited purpose public figure.
It's also possible to become an "involuntary public figure" if you somehow find yourself at the center of something and become a known-entity despite having made no effort to do so, and despite perhaps not wanting to be there.
In both cases, people may find themselves with additional legal burdens if they want to prove they've been defamed, or that their privacy has been invaded, which has made such issues tricky to sort out in an age in which a person can become an involuntary public figure just by wandering into the background of a famous person's photo, by being made into a meme (against their will), or by saying something stupid in private, which is then made public, and which then goes on to shape the trajectory of their lives from that point forward—personally, professionally, and legally.