The Spinola and the Doria were two of the most powerful families in the Most Serene Republic of Genoa. The smiling lady is descended from the first and had married one of the latter, Giacomo Massimiliano Doria, shortly before this portrait was painted in 1606. Her name is Marchesa Brigida Spinola-Doria, and she was 22 years old at the time.
Rubens shows an incredible skill in painting the shiny surface of the satin dress, partly learned from studying Venetian painters, he had travelled through Italy since 1600. The picture is also a good example of the fashion of the time, huge ruffs that make the wearer look a bit like John the Baptist after Salome danced the dance of seven veils.
The painting is now in the National Gallery of Art, Washington, DC. Its description page there has some additional details.