Hi,

PPP (Point-to-Point Protocol)  was mainly used on low speed serial interfaces between locations.  So, if you leased a line from a provider to connect say to sites together, you could run HDLC (which was default encapsulation on serial interfaces) or you could run PPP. With PPP you can use authentication which utilizes PAP (clear text) or CHAP (encrypted).  You can also use PPP over  ISDN lines.  Here is a good doc on PPP authentication:

http://www.cisco.com/c/en/us/support/docs/wan/point-to-point-protocol-ppp/10313-config-pap.html

Also, here is document on how to configure PPP for site to site connectivity. 

http://www.computernetworkingnotes.com/ccna-study-guide/ppp-protocol-and-encapsulation-method-explained.html

Please note that these days Ethernet hand off can give you much higher speed with lower price, serial interfaces are not being used much any more. 

PPoE was used mainly for DSL connectivity.  DSL is also an older technology and not widely used anymore.

http://www.cisco.com/c/en/us/td/docs/routers/10000/10008/configuration/guides/broadband/bba/vlan.html

HTH