It means that you've researched the breed you've chosen, and learned about all the little quirks inherent to that breed. If you're up to these challenges, it can be a very rewarding experience. Puppies are demanding creatures, and aren't able to hold urine and feces for very long, at all. Responsible ownership entails manners and obedience training. Obedience training teaches him to sit on command, and walk in a certain area on-leash.
Responsible ownership involves regular grooming and vet care.
Saints do NOT fall into this category. Breed choice will also determine, to a large degree, the amount you'll spend on vetting your dog. Both of these require planning, and the second requires alot of work. Every time you see a dog chained in a yard, or pooping on the sidewalk without his owner waiting to clean up after him, or running loose down the street, be prepared to take action. If you see a dog running at large, either call the animal control officer, slip a note under his collar explaining responsible ownership, or put a leash on him, and take him home yourself.