A very rough and quick basic explanation if you don't want to read Wikipedia (click on the links)
PNG is a lossless format and and has an alpha channel, in other words, you don't loose data even when compressed and support transparency
.. Cons : big file size
JPG has no alpha channel and looses image data as it compresses, in other words, no transparency in this format, usually exporting it transparency will be replaced by background color in GIMP, light size > download faster on webpages
.. Cons : more you compress less good looking is your image
PNG is a lossless format and and has an alpha channel, in other words, you don't loose data even when compressed and support transparency
.. Cons : big file size
JPG has no alpha channel and looses image data as it compresses, in other words, no transparency in this format, usually exporting it transparency will be replaced by background color in GIMP, light size > download faster on webpages
.. Cons : more you compress less good looking is your image
Patrice