Network routing
In the old days of analog telephones, making a phone call meant a continuous electrical connection from your phone to your friend's. It was as if a wire were run directly from you to them. There was no such wire, of course – the connection was made through complex switching systems – but it was electrically equivalent to a single wire.
There are too many Internet nodes for it to work in this way. We can't provide a direct, uninterruptible path from each machine to each other machine it wants to talk to.
Instead, data is bucket-brigaded – handed off from one router to the next, in a chain, each one bringing it closer to its destination. Each router between my laptop and google.com is connected to a number of other routers, maintaining a crude routing table showing which routers are closer to which parts of the Internet. When a packet arrives destined for google.com, a quick lookup in the routing table tells the router where the packet should go next to bring it closer to Google. The packets are small, so each router in the chain ties up the next router for only a tiny fraction of a second.
Routing breaks down into two sub-problems. First, addressing: what is the data's destination? This is handled by IP, the Internet Protocol, whence IP addresses. IPv4, still the most common version of IP, provides only 32 bits of address space. It's now fully allocated, so adding a node to the public Internet requires reusing an existing IP address. IPv6 allows 2128 addresses (about 1038), but only has about 20% adoption as of 2017.
Now that we have addresses, we need to know how to route a packet through the Internet toward its destination. Routing happens fast, so there's no time to query remote databases for routing information. As an example, Cisco ASR 9922 routers have a maximum capacity of 160 terabits per second. Assuming full 1,500 byte packets (12,000 bits), that's 13,333,333,333 packets per second in a single 19 inch rack!
To route quickly, routers maintain routing tables indicating the paths to various groups of IP addresses. When a new packet arrives, the router looks it up in the table, telling it which peer is closest to the destination. It sends the packet to that peer and moves on to the next. BGP's job is to communicate this routing table information between different routers, ensuring up-to-date route tables.
IP and BGP together don't make a useful Internet, unfortunately, because they provide no way to transfer data reliably. If a router becomes overloaded and drops a packet, we need a way to detect the loss and request retransmission.