As said by others, it's a newer technology led by the industry leader Plaid...but certainly other companies like Yodlee (now Equifax) are getting involved and it's rapidly growing in popularity. But like you, most people are still VERY skeptical of it which is completely understandable.
At this point, the use-cases are primarily for a faster and more secure manner of sending/receiving money between institutions or businesses compared to the older ACH technology (routing #s and account #s), as well as aiding lenders when it comes to the requirement to verify deposits/income in the process of a loan application...usually mortgages.
Credit card companies use the technology to make it easier for cardholders to connect bank accounts and make payments.
Venmo or Paypal now use it to quickly link accounts for sending/receiving payments, as opposed to the old way of entering a checking account info...waiting on the two small deposits to occur, then verifying, etc...which could take days.
When getting a mortgage, lenders can use it to instantly verify recent deposits made to your account, which can speed up the loan approval and closing process (think Rocket Mortgage).
The list of benefits and uses goes on...
There's a lot more to this and I'm happy to answer questions.