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This is a long one so sorry... Basically prior to 1995, the transfer system basically was controlled by the clubs. If a players contract expired, the club could keep the player registered with them demanding a fee for him to move. When Bosman's contract with Liege expired, he tried to move to Dunkerque in France. However Liege refused the move. Liege wanted £500k paid in full up front in order for the transfer to happen. Dunkerque didn't value him that highly. So as they were entitled to do at the time, Liege kept him under contract, cutting his wages by 75% until another club paid the required 75%. Bosman challenged this in court, basically suing Liege, the Belgian FA and UEFA effectively saying the transfer system broke European Law.
The courts eventually sided with him, basically allowing players to leave clubs for free at the end of the contract, this is known as the Bosman ruling.
That gave players a lot more power in contract renegotiations as when their contracts expired, the clubs could no longer command a fee, so wages skyrocketed.
Honestly, this whole topic is rather interesting and there's loads of detailed information on it. It's worth a read. Also another court case worth looking into, Eastham v. Newcastle United