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When we meet someone for the first time, there are rituals in every culture for smoothing over what is actually an unpredictable moment, making it commonplace. The handshake, the smile, the obligatory "nice to meet you" phrases and questions. We are comforted by their utterance, even when we are not actually really listening to them, because we know how this dance goes.
So when someone breaks with tradition and does something else, it can be startling. Perhaps it's subtle: a meaningful pause, not releasing the hand or the eye-contact when we expected to be moving on to the next moment. Sometimes it's mismatched levels of comfort and affection - the greeting kiss in France is de rigeur, whereas in the U.S. it's often perceived as too intimate when meeting a stranger. Imagine you are introduced to someone at a dinner party; what types of greeting would you find comfortable, humorous, engaging, offensive?
The beginning of a piece of music is very much like meeting a new person. The composer can say a lot in the initial moment, signaling what kind of relationship we are about to encounter with the piece. Listen to the beginning moments of Mozart's masterful 40th symphony in G minor:
It begins immediately with a steady and energetic rhythm in the accompaniment instruments (mostly strings here), establishing the pace, as well as the harmony, and the melody comes in - we hear right away that we are in a minor key. Minor + fast pace = drama, and you get the feeling for what kind of musical experience you're in for. Mozart lives up to our expectations, by providing us with an entire movement of theatrical musical motives and continuous rhythmic pace that moves things along.
Now, how would you expect a Violin Concerto to begin? Listen to Mendelssohn's opening, which is very like the Mozart we just heard:
Rhythm and the harmonic world are established by accompanimental stringed instruments, and then the solo violin dives in. "Ahh, a fast-paced dramatic movement with a fancy violin solo on top! Just as I expected."
The composer is making choices about how to say hello, and setting up expectations for the audience, through his choice of tempo, harmony, and his choice of the particular instruments he uses to relay all of this information.
So imagine the audience assembled in 1806 to hear the premiere of Beethoven's Violin Concerto. There is a certain greeting ritual they are expecting as the orchestra gets ready to begin. And then the first sounds they hear are not a typical fast-paced tempo, not the accompaniment in the strings, not even the solo violin just diving in. Instead, Beethoven chooses to begin this entire piece, ostensibly featuring a violinist, with a timpani solo! Four simple, unhurried strokes on the timpani replace everything we know about how to shake hands with a violin concerto. Immediately, the audience is startled into paying attention: what is going on here? What is about to happen? Where can this piece of music possibly go to, if this is the starting place?