This version can now be found in the Sala di Apollo of the Palazzo Pitti in Florence, with the other later painting to be found in the Hermitage Museum in Saint Petersburg, Russia. The colours are not quite as strong in this earlier work, but this may be due, in part, to the additional few years that it has lived through. There are also a variety of different digital reproductions of it which have different colour balances and you can only really get a true sense of it by visiting the original yourself.
Titian would typically sign his works as TITIANUS and you will see that in this painting he has inscribed his signature into a small ointment jar in the bottom left corner of the canvas. On many occasions he would attempt to somehow blend his signature into an element of the scene. See also the other version, titled Penitent St Mary Magdalene.
The theme behind this painting is where Magdalene has sinned and fallen but finally returns to the path of Jesus, which is the right path. She is depicted with little or no clothing in this artwork, though there is no sexual element to this - Magdalene spent years in the desert after the Ascension of Jesus and as a result she was left wearing rags. She had symbolically given away her jewels and other luxurious items in order to concentrate fully on her devotion to God, having discovered the errors of her ways.
The overall tale behind this work is common to many religions, where your path can be lost if you become distracted by some of the things in life that ultimately don't matter - namely material goods. Sometimes people require reminding of how to follow the right path, and can be actively lead towards the right route.