It sounds like something from flatmate hell, where the first person to move into a shared house gets the advantage of choosing the best room, or from sport where the racer first off the starting block has an advantage.
In fact this business term originated in the game of chess, where there is a slight statistical advantage for white who has the first move.
In the business world it has come to mean the advantage gained by the first significant company into a new market. Very often the “first move” has some transforming aspect to it, or combines two formerly separate products or services.
One commonly cited example is Netflix, a DVD rental service that outmanoeuvred the incumbent video rental giant Blockbuster. By developing a huge supply of DVDs, a fast delivery service, and a very simply business model that could be explained online Netflix could take over the market for DVD rentals in the US.
Apple are also often mentioned, although they did not develop MP3, and were not the first to think of portable music players (I had a Sony Walkman way back), they combined the two into a device that people would actually want to use, and developed an online delivery model, iTunes, that has left the rest of the music industry scrambling.