The London Tube map works because it deliberately lies about geography.
In 1931 Harry Beck, an Underground employee working in his spare time, realised underground passengers don't care where stations really are, only how they connect. He drew the network with straight lines at 45° and 90° angles. Bosses were sceptical, the public loved it, and he was paid about ten guineas.
Early London Underground maps drew the lines over a real street map. The result was crowded in the centre, and the outer ends of lines often had to be cut off to fit. By 1920 the designer MacDonald Gill had removed the background detail, but the layout was still essentially geographic.
Harry Beck, an Underground employee, saw that for a passenger underground, physical position hardly matters; what matters is the sequence of stations and where you can change. In his spare time in 1931 he drew a diagram with straight line segments running only horizontally, vertically or at 45 degrees, let go of true distances, kept the River Thames as the one landmark, and marked interchanges with diamonds. Colleagues noticed it resembled an electrical circuit diagram, and he once drew a joke version with circuit symbols.
The Underground was doubtful about an uncommissioned side project and tested it in a small pamphlet in 1933. It was immediately popular, and topological maps have been used ever since. Beck was paid ten guineas for the card version and five for the poster. He kept revising it until 1960, when he fell out with a publicity officer who produced his own, more cramped version. Beck's contribution was officially recognised in 1997, and today's maps carry a line crediting his original 1931 design.
The trade-off is that the map can mislead about the real distances and directions between stations. When the Thames was dropped in 2009, the outcry was so great it was restored within months. Beck's approach, straight lines, fixed angles and evenly spaced stops, has been copied by transit maps around the world, and in 2006 the Tube map was voted one of Britain's top ten design icons.
Source: Wikipedia — Tube map · Text summarised from Wikipedia (CC BY-SA 4.0)