An online shopping cart is designed to mimic using a real-world shopping cart in a physical store.
When you go to, say, a grocery store, you get a shopping cart of your own just like every other customer. Each shopper's cart starts out empty, then it accumulates items as they add items to their own cart. You can leave your cart for a little while and come back to it, and all the items you'd put into it would still be there, but if you abandon your cart for too long without coming back to it nor taking it to a cashier, eventually the store will round it up and put the items back.
Each buyer using the cart buttons on your site would get their own "virtual" cart, which would start out empty and only accumulate the items they deliberately add to it. Any buyer can keep a collection of items, coupons and shipping settings in their cart for up to 24 hours after their last cart view. If that much time passes without viewing their cart nor taking it to checkout, their cart would get reset, so they'd need to start over next time they return to your site -- just like if you go to the grocer today, you wouldn't expect to find a cart full of items that you'd abandoned in the aisle yesterday.