There are many different forms of "social partner dancing" but they have have 3 things in common:
The dance is done between 2 people, who dance the entire song together in an (almost) embrace called "dance frame."
One person is a leader and the other the follower; the leader choose the moves spontaneously and the follower follows along. This non-verbal communication is called "lead and follow." It is not a set pattern.
Each dance has a specific rhythm pattern and is marked by a distinct foot pattern. Different dances fit different styles of music.