I see the value of paypal, which is to create a screen between me and a dodgy website which I am buying from. That website can't get my credit card number and therefore take further payments. But when I am making a payment to someone why should I need an app to protect me against fraud? So I don't get the security aspect either.
I have Bank of America. For the same transaction to happen I would need my friend to sign into his bank account on a mobile phone, initiate a wire transfer from his checking account to my checking account, which requires me to provide him my checking account number and zipcode and full name.
And that's just a 1 on 1 transaction.
The most common use case is if I'm eating in a group of say... 6 people. Instead of splitting the bill 6 ways which many restaurants won't allow one person will front the bill. The rest of the group just "Venmo's" the person who fronted the bill whatever they owe. No exchange of account numbers, no asking for Paypal email address, none of that. The assumption is that everyone has Venmo and everyone's connected on Facebook. As long as those 2 facts are true (which is common for American millennials) the convenience is bar none.
Most people wouldn't remember a number like a checking account number nor do they carry checks around with them. Venmo is simple and easy for them to send money to friends without having to log into a bank's shoddily designed website and figuring out how to transfer funds which is probably non-obvious in the first place.