There are two things these sites do: DNA sequencing and genealogy.

Genealogy is a big field. Lots of people, both professional and hobbyist, spend hours combing over public records or walking through graveyards, taking careful notes. They build very detailed records of who is related to who based on these records.

But those records are often incomplete. Sometimes the father isn't reported at birth. Some children are born in secret and not recorded. Sometimes birth records are falsified. Genealogists ALSO try to figure that stuff out. Sometimes people who find out their parents weren't biological hire detectives to try and put together where they came from. If that gets back to a genealogist that can help them piece together more accurate records. (I had this happen, I found out when I was around 19 that certain aspects of my family tree were lies to cover up some things a different family member was too embarrassed to admit.)

The most extreme cases are things like the fertility doctor who was using his own sperm on patients instead of the donors they had selected. There are dozens of people we know have incorrect biological lineage because of him, and we're not 100% sure how many more there might be because he wasn't consistent and even he can't remember every time he did it.

DNA sequencing helps do that. If it finds a close match, some detective work might reveal there was a birth that wasn't reported properly. Sometimes it's just coincidence. Sometimes the people who know the truth all dead. But generally if people match enough and have parents who were geographically near each other roughly 9 months before their birthday it's not a stretch to assume there might've been a misreported birth.