All levels
"Cabeceo - What are you talking about?"
In social tango, the cabeceo is the most common invitation to dance. The method: a dancer, playing the leader role, looks for eye contact with the desired follower. When it happens, the leader nods as an invitation to the dance floor. If the followers agrees, nods back keeping the eye contact. After that the leader goes to meet their dance partner.
Where does it come from?
The Cabeceo is really an argentine cultural thing that goes beyond tango. Eye contact followed by nodding is a traditional argentine seduction manner. One was able to see it almost at any social event early last century (when the golden age of tango took place). This cultural behaviour still takes place over there, although it is not often seen among the young crowd.
To do or not to do?
The leader can still go and directly ask to the follower to dance, although if there is no wish to dance, the leader might get into an uncomfortable position or end up forcing the follower onto the dance floor (when a follower refuses the leader, Part 2).
Pros & Cons
Safest way to invite for a tanda: when the follower agrees, all good. When they do not agree... all good! (ok, almost) but at least you won't feel embarrassed at all.
Going to invite for a dance standing in front of your follower, chances of success are higher, so is the risk of embarrassment. Also, it can be seen as a rude approach.
Ok, cabeceo does not have it all. When in crowded milongas or oddly shaped venues, the cabeceo can not be our best friend. So, leaders should try to get closer to the follower but still look for a clean straight line between them both.