They failed to embrace online, that was their downfall. They didn't take it seriously, opting to let someone else handle online for them, one of the largest players in the ecommerce space: Amazon.
It goes back to the year 2000 when Amazon and Toys R Us signed a 10 year agreement that would make Toys R Us the exlusive vendor of toys on Amazon. So what happened was when you would click on toysrus.com it would send customers to their page on Amazon.
The deal started to fall apart when Amazon started allowing other toy retailers to sell through its site, because they complained Toys R Us didn't carry enough stock. So, they sued in 2004 and terminated the contract, then did its own online thing in 2006.
Coincidentally, the same thing happened with Borders (the large book store chain) which had a similar partnership with Amazon, lost out on embracing online and owning the entire workflow of selling online. Essentially Amazon was the site customers would see when ordering from these retailers.