This cliché first developed in the 18th century and means to take over somebody’s idea, fame or recognition or to draw people’s attention towards oneself at the expense of someone else. The phrase originates from the theatre at a time when new methods of creating stage thunder were being invented.
Writer and critic John Dennis invented one successful new method of creating the sound of thunder on stage for his play Appius and Virginia in 1709, however his play was a box office failure. The invention of the sound effect however proved very popular and was used immediately afterwards in a highly-praised production of Macbeth applaud.
This frustrated John Dennis greatly and he apparently said: ‘Damn them! They will not let my play run, but they steal my thunder’. It seems that this was the origin of the phrase, so at least Dennis created something that definitely lasted!