I used to set these everywhere I construct a new router to my costumers, but i don't know what they are for.
VPI is Virtual Path Identifier and VCI is Virtual Channel Identifier and are used by, and are specific to, the ISP and differ per country. Typically in the UK these are 0 and 38 respectively.
PPPoE is Point-to-Point Protocol over Ethernet. PPP used to be the method dial-up modem ISPs used to bring TCP/IP and authentication over a telephone line. PPPoE is just a next generation of that using Ethernet lines.
LLC is Logical Link Control, a means to transfer TCP/IP or IPX over a line.
VC-MUX is Virtual Circuit Multiplexing and is an alternative to LLC but does much the same thing. So LLC or VC-MUX will be determined by the ISP in question.
CHAP is Challenge Handshake Authentication Protocol and is used to securely authenticate the username / password account to sign-in to the ISP.
Hope that sheds light on their purpose.
Vpi VciSource(s): https://shrinkurl.im/a87Ok