The work being performed was Johann Sebastian Bach's St. Matthew Passion. The conductor was Felix Mendelssohn. These two men seem an unlikely pair--one was the son of a town musician, the other the son of wealthy banker. One was orphaned at an early age, the other had a happy, stable childhood. One was from a strong Christian background;
the other, despite his Jewish heritage, was initially given an explicitly non-religious upbringing, until his father decided to offcially convert to Christianity to overcome the prevalent anti-Semitism of the time. Nevertheless, the two men were destined to be closely linked in musical history.
Perhaps the most obvious link between Bach and Mendelssohn is the role the latter played in promoting a revival of interest in the former's music. Until Mendelssohn's performance of the St. Matthew Passion, Bach was not well-known to the general public--although he was known to professional musicians. The 1829 concert changed all that. Today, in part due to Mendelssohn's unflagging advocacy, Bach is almost universally acknowleged as one of the greatest of all composers in history. In addition, a number of his works, like the Brandenburg Concertos and the Orchesral Suites have become staples of the concert hall, his keyboard works like the Goldberg Variations and the various suites are now an important part of standard keyboard repetoire, and his organ works are foundational for organists (not to speak of his chamber and choral works!).
In addition, while Mendelssohn could be said to have had a major influence on Bach's posthumous reputation, he in turn was influenced by Bach. That influence can be seen in both the types of music Mendelssohn composed and the techniques he used in his compositions. Thus, for example, Mendelssohn's cantatas show the influence of Bach's choral works. At the same time, in many of his compositions Mendelssohn employed contrapuntal technique--one of the best-known aspects of Bach's music. Bach may have even had a spiritual influence on Mendelssohn: according to Patrick Kavanaugh in his book Spiritual Lives of the Great Composers (p. 77) , at one point Mendelssohn was attracted to Catholicism, but his devotion to Bach caused him to remain a Lutheran ( Incidentally, I have seen one website claim that "religion was not important" to Mendelssohn--on what basis I don't know. I can't help wondering whether some historical revisionism was at work! Kavanaugh in his book quotes the French composer Hector Berlioz, a freethinker, as saying that he shocked Mendelssohn by his irreverent attitude toward the Bible).
Finally, there is a similarity in the two composers' places in music history. Both Bach and Mendelssohn were essentially musical conservatives who creatively incorporated the best of the past in their music.
In short, despite the differences between these two great musicians, it can be seen that there was a profound connection between them. Thanks to that (providential?) connection, the world has been blessed with some magnificent music.