A PNG stores the picture exactly as it is given, so every later save leaves it unchanged. That matters when a picture is about to be cropped, retouched, or pasted into a design several times over. Some printing and design tools also refuse a JPG outright.
What the change costs
The file gets larger, often several times larger, because nothing is thrown away any more. It also does not undo what the JPG already lost. The blur and the blocks around sharp edges are part of the picture now, and a PNG preserves them faithfully.
When to do something else
Converting a photograph to PNG just to store it wastes space and gains nothing. Do it when the picture is going to be edited, and not as a way to improve one that is already saved.