Music is almost always performed for the purpose of conveying a particular meaning. Music composers, lyricists, conductors, think in terms of the meaning they wish to convey when they write the music, pen the lyrics, and conduct an orchestra. Conductors are judged in no small part on how they configure an orchestra and how they emphasize certain passages within a movement. They may convey a message by elevating winds or brass or percussion, or, conversely, by minimizing a particular section or instrument.
Especially with regard to classical music, the meaning that the composer is trying to get across can only be determined through careful analysis by someone with a very fine ear for music. Take, for example, the below passage from an essay on Mozart's Sonata facile K. 545:
"While the comprehensible formal structure in Mozart's music is relatively easy to follow, the meaning and content is far more difficult to grasp for the modern listener...Is it possible that Mozart wishes to convey more than just an expressive melody? Even the few notes at the beginning of this work prove to be more eloquent than one might think."[Jochen Reutter, On Mozart's Musical Language]
Later in that essay, the author observes that "Mozart's occasionally brooding pauses should rather be placed into a dramatic context."
So, divining the meaning that a composer is attempting to convey in classical music takes considerable training in the structure of music and in the idiosyncrasies of that particular composer.
Classical music, because the vast majority is instrumental (obvious exceptions like opera, Beethoven's Symphony #9, Handel's Messiah aside), understanding the meaning the composer is trying to convey requires study. Similarly, instrumental jazz also requires careful study to divine meaning, although the music of Miles Davis differs considerably from that of Charlie Parker, with their respective personalities audibly visible in their playing.
Other forms of music require less patience. When Johnny Cash sings about "walking the line," anybody familiar with his biography understands the context and meaning of the words as they come out of his mouth. Mick Jagger's lyrics to accompany Keith Richards' compositions frequently reflect their history as musicians, partners and occasional rivals.
Conducting music is an art form. A conductor works with the orchestra to ensure that it performs each passage of each piece precisely how he wishes to communicate it to the audience. When orchestras change conductors, either voluntarily or involuntarily, it almost always represents a change in how the same pieces will be performed, according to the personal proclivities of each conductor. The following quote from SB&O Magazine describes the situation well:
"The quality of musical sound that is produced by an ensemble is greatly affected by a conductor's gestures, body language, and facial expressions -- nonverbal cues. This may partially explain why different conductors obtain different results and sounds from the same performing ensemble."["Rehearsing Music: Nonvergal Cues, Body Language, and Facial Expression," SB&O, June 1, 2009]