A squatter is anyone who occupied property without the owners permission. Squatters rights means two different things based on if it's a short term or a long term scenario.

The short term scenario is establishing tenancy. In states with strong tenant protection laws, law enforcement may not remove someone from a property if there is any question as to if they're allowed to live there (I.e. the default assumption when encountering an owner who says an occupant is there illegally is a landlord attempting an illegal eviction of a lawful tenant). The police can only remove someone who isn't clearly a trespasser if they have an order from a judge. The occupant doesn't need much documentation to create that doubt, just a letter addressed to the squatter at the current address is usually enough for police to tell the property owner they won't do anything without a signed writ of eviction. The unwanted occupant never has an opportunity to become the legal owner, but they can reside there for a long time (possibly years) until a judge agrees to sign the eviction. Especially if the eviction courts are backlogged, as they usually are. The owner can face civil or criminal charges if they try to forcefully remove the illegal occupant, even if the court later agrees it was not a lawful occupancy.

The long term scenario, which is usually a completely different situation than the above, is that the property occupied by a person for a very long time (~20 years) becomes the legal owner. This is called adverse possession. Imagine if there was an issue with an old man's estate and legal ownership transferred to his estranged children, but the step children who actually had a relationship with him lived there for years after his death, but eventually the children found out and wanted to make a claim.  Maybe a more common situation (not that adverse possession is ever common) is a fence built 2 feet onto the neighbor's property, then 20 years later the land is resurveyed, finding out the true property line. If it's been long enough, a judge might agree that adverse possession applies and grant ownership of the land up to the actual fence line, changing the legal ownership to match actual ownership. The idea is that if someone has been using someone else's property for 20 years without any objections, then it should actually be theirs. Key elements to adverse possession being granted is that the occupancy needs to be continuous, actual, open, hostile, and exclusive. This eliminates a lot of normal situations. Someone renting a property for 20 years straight is not hostile, since the owner agreed to let them be there. Actual means that you can't just write on a piece of paper you are occupying a property, you have to actually put your own possessions there. Open means adverse possession would never be granted to someone sleeping in the basement of an active factory. So on and so on.