The generally accepted meaning is: when someone takes something or an idea that is yours and uses it as their own, often in a demeaning way
The history behind the saying goes way back to 1704 London when John Drury, a literary critic and part-time play write produced his play, "Appius & Virginia" and used a new method of replicating the sound of thunder.
The play was unsuccessfully and was closed down. A short time latter, Macbeth was produced and his new thunder method was used.
Drury was none to happy about this and in an 1893 publication called, "W.S. Walsh's Curiosities", Drury is quoted as having said, "Damn them! They will not let my play run but they steal my thunder!"
"Hey honey, I learned to ride a horse today!" (all proud, excited and giggly.
"Well, when I was only five I was riding, trotting and galloping....all bareback! "
She definitely could be said to be trying to steal my thunder
"Hey Gramps, I learned to ride the number 3 bus and transfer at First and Elm, buy tokens at the kiosk and get on bus 7 and ride all the way to school today!" (another all excited, giggly moment of self-pride)
"Well, when I was your age, I had to walk four miles...one way...in snowstorms and hail"