Passengers 
are generated and consumed by buildings in towns if these buildings are within the coverage area of a station, and that this station provides passenger traffic to other stations near towns. You use trains or buses to transport passengers between such stations.
The "Passenger destination" of May 2020 implemented a game option (enabled by default) where each passenger wants to travel to a specific town, and not just anywhere. Each passenger is assigned a destination town, and will find its way through your network to reach this specific destination. With this update the passenger economy changed considerably: The game keeps track of which other towns your network provides passenger service to (directly as well as indirectly), and generates passengers for those other towns - and only those towns. In other words, if a town is not reachable from your town, passengers wanting to go there are not generated and never appear at the station. This means that towns that are connected to many other towns generate many more passengers.
So if you build lots of simple loops (town A <-> town B, town C <-> town D, town E <-> town F and so on) you will see a (relatively) small number of passengers (especially if you start your game with the game setting small towns). But if you then connect, say, town B to town C, you will experience a large increase in passenger traffic. For instance, now town A not only generates passengers wanting to travel to B, but C and D as well. If you then connect town B to town E as well, passengers from all six cities can reach each other through station B - which translates to a massive increase in the number of passengers that want to use your network: while most passengers from town A might still want to travel to the nearby town B, the new passengers interested in towns C through F (that they reach through station B) will likely multiply your overall income several times and fill your trains.
Upon delivery passengers generate money tokens 
. The amount of tokens generated depends on the distance between the towns passengers are transported to and from. The game measures the distance as a direct line between those towns, not the actual length of the rail tracks. You are paid when a passenger reaches its final destination, not for each stage on its journey.