(I am just going into the basics, so ignore gross errors.)
It just fakes a cell tower. Because of the nature of how modern radios work, a phone will likely connect to the strongest signal it detects. The stingray acts as a “man in the middle” and relays the phone signal to an actual tower as if it was the original phone making the call. As it relays the call, the operator can listen in.
It’s akin to answering a call, making a call on another phone and then holding the two phones together.
(MITM attacks on HTTPS connections are similar, but there are some nuances with how the connection is decrypted and the re-encrypted.)