How does the Paypal 'Mobile Phone and PIN' login work?
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.