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The network trained on thousands of dog photos. After enough passes through the data, it gets every single one right. That sounds like success.
But here's the million dollar question: did it learn what a dog is, or did it just remember the photos?
Those are not the same thing.
A network that has genuinely learned something should be able to look at a dog it has never seen before and still recognize it. One that only memorized its training examples will fail the moment you show it something new.
From the outside, both look identical during training. Both get the answers right. The difference only shows up when you test them on something they haven't seen.
This is the central problem of training a network. Getting the right answers on your training examples is easy. Getting the right answers on everything else is the hard part.