Interesting topic. It doesn't just happen at gigs, quite a few songwriters preface songs or lyrics with the story of the lyrics... kind of a pre-emptive strike. To me your lyrics either contain enough to connect with in the way the writer wants or they don't. A wriyer prefacing in this way I think is ofyen the result of the lyricist being regularly asked about their songs, and rather than improve their writing to address it, they feel a need to justify it and explain it in order to head off potential negative comments. Don't get me wrong, not all songs need to answer all of the questions they pose and sometimes leaving something unexplained can promote discussion... but if that is intentional... why explain before people hear or read it? That just doesn't make sense.
Talking is certainly a common way to establish a connection at a gig. You know, "A funny thing happened on the way to the gig...." etc. Perhaps it's that the need for something to say to the audience, accompanied by a lack of anything interesting to say, is satisfied with the story of the song? Killing two birds with one stone.