The Pontifical March was composed by Charles Gounod in 1869. In 1949 it became the official anthem of the Holy See, replacing the Marcia Trionfale of Austrian composer/bandmaster Viktorin Hallmayer. I've been unable to find a video of the old anthem, but from all accounts the Gounod is a great improvement. What I like about it, is that depending on interpretation, tempo, instrumentation etc. it is adaptable to the mood and atmosphere required at different occasions, be they solemn or joyous. Even so, it can sound banal and clunky if played without any flare or imagination. It will be interesting to see which band is chosen to play it when the Holy Father arrives in Scotland. (I preseume it WILL be played.and I also wonder whether it will be followed by the Scots' National Anthem, or that of the United Kingdom.)
More details of the history of the Pontifical marches/antems are to be found here, together with words in Latin, Italian and English translations thereof.