Logo

Only the first response is accurate, but might not be understood by a newcomer.

In simple words, if you create a Vector image be it in illustrator, Inkscape or any vector-based software, it means you can resize your vector-image even by zooming in a hundred times, and it won't lose its quality, it will preserve its sharpness and clarity, which is why Logos are done as vectors, because they might be needed to be magnified to be printed on a whole building, so if it was a JPEG/PNG image it will get distorted and blurred and will look smudged and unworthy to be used.

On the other hand, if you magnify a vector a million times, it will look as good as the original one, hence Logos are created as Vectors, .AI or .SVG as an example.

For every other Photo-processing, effects, paintings, editings, then Photoshop/GIMP are the answer.

For drawing Mangas and co, then you should use specialized software like Paintstorm.