Why convert JPG to PNG?
Every time a JPG is edited and saved again it loses a little quality. PNG is lossless, so it is a safer format while you are still working on a design. Some design tools and print shops also prefer PNG.
Note that converting does not remove the background or make it transparent. It changes the file format only.
Questions
Why is my PNG bigger than the JPG?
PNG stores every pixel exactly, so photos become larger. That is normal.