"Showrunner" is specifically a TV word, it isn't generally used for films or plays.
A showrunner has overall creative and managerial oversight for a TV series. Individual episodes may have different writers, director, or even producers. The showrunner is above the directors of individual episodes, and ensures consistency or creative vision, and the fair distribution of resources across a series.
It is a modern term. In older TV shows, the showrunner would be credited as "Executive Producer", and on British shows just as "Producer". However a showrunner tends to have more creative input than a producer would typically have had.