I am under the impression that first chair is the seat reserved for the best player of a particular instrument. Second chair would be reserved for the second best.
Is that all there is to it? Or does the position of the chair provide something different to the audience from the 2nd chair? Perhaps it is louder? Or is there anything else that the chair numbers mean?
First Chair is a position of distinction that will usually go to a highly competent player...though not necessarily to the best player in the section. The first chair is also leader of the section...the rest of the section will take their cues and direction on inflection, dynamics, bowings, etc. from the first chair.
The physical location of the chair with respect to the rest of the section is somewhat arbitrary, but generally developed to give the rest of the players in the section good sightlines to the first, and to place that player in prominence to the audience. It is a place of distinction, after all.
The first chair isn't necessarily "up for grabs" every time a new player joins the section...most ensembles/orchestras don't use "survival of the fittest" fight club rules to select the chair. Factors such as longevity with the section, accolades, effectiveness as a leader, etc. come into consideration along with virtuosity.
Adding to the answer from dwoz --
In the string sections, the first chair plays the solos. It's helpful to be able to keep a cool head, and to have just a bit of a strong ego.
The first chair might organize a section rehearsal.
The first chair does a bit of conducting through movement, to help all the section members make their entrances together.
One point I would disagree with has to do with location. The physical location is not at all arbitrary. The principal (=section leader or first chair) sits in, precisely, the first chair -- closest to the conductor, and closest to the audience.
In the percussion section, the principal percussionist will decide who's going to play which part in a particular piece, and will take the critical part him or herself, for example the snare drum in Ravel's Bolero.
I am a first chair Cellist in Honor Orchestra. Usually what first chair does is lead the rest of the section. If there is a solo, first chair is usually the one to be chosen. But doesn't mean first chair would always take the solo. sometimes a 3rd chair cellist handles the solo if capable.(we have a separate test to see who is better before the director decides who they should assign the solo part to). 1st chair player gets a chance to point out what the rest of the section did wrong. For example, tuning and fingering. We get to discuss with the section what to practice for homework as well. Being first chair is kinda like being a mini director for your section.
I would add something to the discussion as well. Dwoz had an excellent answer. There is also a bit more as to what parts the chairs play.
Here is an example; the Horn section traditionally has four chairs (five, but we will get to that in a second. In older works it is divided up into two groups of a high and a low horn. 1st and 2nd as high and low respectively, then a second group of 3rd and 4th as high and low. This changed in history as Horns became chromatic, and then the first chair was high, the fourth was the low, and the middle two played both as needed!
(The assistant horn chair is a part that has to play as well as the first. When the principal (as the first chair is called) has a big concert, the assistant will play some of her parts. The tutti sections, off-beats, or anything not a solo. But he, as the assistant, has to be ready to jump in at anytime if the principal says too)
But as for the best player... I have to disagree with that part. In any profession, is the best person the boss? Well, not always. Yes, the better players tend to rise to the top of the chair numbers, but that hardly means that the First chair is always the best.
The first chair is basically the best player of the section. That means that the person in that chair has an opportunity to teach the rest of the section how to do certain things. For example, an orchestra: the first chair would be the example of the bowing and fingering. For band: fingering and some other things. But besides that, the first chair is the best player.
I play first chair in a mostly professional band. I take the solos. I quiet the band and bein the tuning process before the concert. I often am featured soloist. Sometimes I discuss odd fingerings with others in the section, but I don't teach them anything. They are mostly pros and all are good.
