Wikipedia has this to say:
"Veronica" is a single from Elvis Costello's 1989 album Spike, co-written by Costello with Paul McCartney. The song "Veronica" was co-produced by T-Bone Burnett and Kevin Killen, and features Paul McCartney on his iconic Höfner bass. In 2004, Entertainment Weekly voted it as one of Costello's top ten greatest tunes.
The song focuses on an older woman who has experienced severe memory loss. Costello's inspiration for this song was his grandmother, who suffered from Alzheimer's. When talking about the song on a VH1 interview, Costello reminisced about his grandmother having "terrifying moments of lucidity" and how this was the inspiration for "Veronica".
"Veronica" was also Costello's highest-charting Top 40 hit in the United States, peaking at #19 on the Billboard Hot 100 singles chart, #1 on its Hot Modern Rock Tracks chart, and #10 on its Mainstream Rock Tracks chart.