It's a really funny saying. It was used a lot in the Pixar movie 'Cars'.

win praise for oneself by preempting someone else's attempt to impress.

In smaller words, Thunder is really loud and gets attention. So, 'steal my thunder' means, 'you are taking away my glory'. 'i was going to be impressive, but you took it away'. 

It's an idiom. So it is hard to understand. Does that make sense? 

Savannah gave the meaning. The phrase derives from the device used in theatres to make the sound of thunder. The following articles gives the pertinent facts:

<a href="http://www.phrases.org.uk/meanings/steal-ones-thunder.html">http://www.phrases.org.uk/meanings/steal-ones-thunder.html</a> ;