What they show is how far you can travel in a 24 hour period using only trains and brisk walking from a collection of 28 European cities. In a few cases, such as from London to Dublin, a ferry ride is also included.
Here’s a zoom in on London:
The obvious takeaway is that Western Europe is very well connected, whereas many parts of Eastern Europe are not. Some cities, such as Tallinn (Estonia) and Podgorica (Montenegro) are almost completely disconnected.
Of course today there’s stiff competition from air travel.