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.