With a "My Basket" you go to the store and do your shopping in a regular cart or basket, storing your "My Basket" underneath. When you get to the cash register, you hand the cashier your basket and they then load all your groceries into the basket, rather than into bags. When everything is in the basket, the cashier tapes a paper over the top to indicate the groceries inside have been paid for and you're on your way.
The biggest problem with the basket so far is that even though everything fits inside, it is too heavy for me to carry. So I usually end up taking a backpack or tote bags in addition to distribute the weight. I also can't help wondering how many plastic bags went into making my pink plastic basket.