The Paypal app has a two ways you can log in, 'Email and Password' and 'Mobile Phone and PIN'.
How does the second one work? I can't seem to set a PIN code myself and it doesn't use the one from my phone.
First off, you gotta login to the PayPal app on your phone.
(In this case, obviously, your Android device ;) )
Next up, you gotta visit your PayPal account settings through your web-browser
(The gear on the top right)
Then, you gotta go over to the "Security" tab and click on "Mobile Devices"
From there on you should be able to figure out how it works.
I haven't linked my mobile with PayPal yet, so I can't help from here on.