Facebook operates a vast global network connecting its datacenters and points of presence (POPs). When you connect to Facebook from, say, Tokyo your HTTPS connection is terminated in a local point of presence (likely in Tokyo or somewhere in Japan) and from there the connection is forwarded on to a datacenter in the US or Europe. This forwarding happens over Facebook's privately operated network backbone, which needs to be substantial enough to handle billions of users' traffic (not to mention internal replication traffic and so on). Renting capacity from commercial providers is expensive so Facebook and the other big tech companies are interested in building their own infrastructure for this purpose.
Of course, it would be possible to have a user in Tokyo connect to Facebook's network somewhere closer to the DC but a) getting onto FB's high quality, low congestion network ASAP will perform yield much better performance than leaving the connection running over the internet where it's subject to congestion and long SSL connection round trips, b) terminating user sessions in POPs allows much finer control over which datacenter users are ultimately sent to. Without this FB would have to rely on DNS changes to steer traffic and they are slow to propagate and crude.
Of course, it would be possible to have a user in Tokyo connect to Facebook's network somewhere closer to the DC but a) getting onto FB's high quality, low congestion network ASAP will perform yield much better performance than leaving the connection running over the internet where it's subject to congestion and long SSL connection round trips, b) terminating user sessions in POPs allows much finer control over which datacenter users are ultimately sent to. Without this FB would have to rely on DNS changes to steer traffic and they are slow to propagate and crude.