The phrase "to ditch the diapers" means to stop using diapers, which are used for babies to collect their waste, and switch to using a toilet like older children or adults. Full definition
You might be in a hurry to ditch the diapers once your daughter reaches her second birthday, but not so fast. (howtoadult.com)
I was determined to stick with it, but wasn't quite ready to ditch the diapers altogether, so I started researching solutions. (vibrantwanderings.com)
This means you can ditch the diaper bag which although useful in certain situations, it's an annoyance when hanging from the handlebars and generally being bulky and in the way. (mombible.com)