This is a term that heard when I first started dancing. That is, with the average song length considered to be approximately three minutes (well, okay, lots of salsa and hustle songs are much longer), what you have with a dance partner for the period of that song is a “three-minute relationship.”
So, if you ask (or are asked by) a partner to dance, that is not a request to marry, date or hook up – it is solely a request to share about three minutes of time together on the dance floor.
If you are asked to dance by someone with whom you prefer not to partner or, after beginning that social dance – whether you are a follower or a leader – and it is not going well (for whatever reason), remember that it is only for about three minutes – just smile and get through it.
On the flip side, if it is an enjoyable experience, make the most of that “three-minute relationship” – perhaps you can share other dances!