Blues and Swing are both forms of dance usually done with a partner, similar in style and form. Generally, they are the forms of dance done along with blues and big band jazz music. These forms of dance fell out of style with the advent of rock and roll, particularly with the arrival of the Beatles. As swing music fell in popularity, so too did partner dancing. For more formal definitions, here is what wikipedia has to say on the subject.
What is Blues and Swing Dancing?