These photos are of a replica of the first Traveling Post Office which started in 1838.
The nets collected bags of mail as the train went by (without stopping, of course). After the Great Train Robbery (1963) the mail coaches were designed with smaller windows and mail clerks were required to keep the doors locked when the train was stopped. (The robbery netted about $74 million in today's dollars; little of it was recovered.)
Whole cars were devoted to mail sorting.
Traveling Post Offices lasted until 2004 when the Royal Mail discontinued moving mail by train. (They've recently restarted some railway-based service.)