Lyric discussion by Stickysen 

Cover art for Jenny Wren lyrics by Paul McCartney

I found this info about the song on Wikipedia:

Jenny Wren was written in Los Angeles, and is about a character of the same name from Charles Dickens' novel Our Mutual Friend. It also refers to an English bird known as the wren, which is reported to be McCartney's favourite. McCartney wrote the tune in the same sort of finger picking style found in "Blackbird", "Mother Nature's Son" (The Beatles) and "Calico Skies" (Flaming Pie).

Song Meaning