I'll just copy paste an email conversation I was having with a tech support guy for my tuner. He's answering a specific question I had but it goes into temperaments and there are a few links that deal with the subject. But in the most basic sense, they are slight adjustments made to note frequencies. The purpose of them is to make an overall "better sounding" range of notes.

On the ST-200, each of the 5 settings other than Chromatic (CHRM) can be set to one of two modes, "open tuning" mode or "temperament" mode. In open tuning mode, the tuner shows the string number of the note being played. In temperament mode it shows the note name, and will respond to all 12 notes of the scale. In either of these modes you can offset each note by up to 50 cents.

CHRM mode is always equal temperament chromatic. The other 5 settings can be programmed any way you want.

As shipped, the tuner is set to open tuning mode, and there are no cents offsets programmed in, so you will be tuning in equal temperament. You can customize them any way you want. You can also change any of the 5 programmable settings to temperament mode. In this mode the pre-programmed temperaments shown on page 24 will be in effect. Again, you can customize the offsets any way you want. The temperaments we include are used by guitarists that play special instruments. I will discuss some of these shortly.

Just Intonation is a musical scale where the intervals between notes are based on ratios of integers. For example, the interval of a fifth has a ratio of 3/2, and a major third has a ratio of 5/4.

These intervals are also called pure intervals. They give a very harmonious sound.

For example, middle C has a frequency of 261.626 Hz. The note E is an interval of a third away, and so will have a frequency of 261.626 x 5/4 = 327.032 Hz. Similarly, the note G is an interval of a fifth away, and so will have a frequency of 261.626 x 3/2 = 392.438

An excellent discussion of tuning and temperaments can be found here: http://www.guyguitars.com/eng/index.html

You can learn more about Just Intonation at http://www.justintonation.net/

A musical temperament is a method of tuning that makes adjustments to the pure intervals of just intonation. You can find a discussion of this at http://en.wikipedia.org/wiki/Musical_temperament

The equal temperament is the most common one today. It divides the octave into 12 equally spaced intervals (a semitone) which correspond to one fret position on a guitar, or one key on a piano.

Each semitone is further broken down into 100 units, called a cent. In other words, one cent is 1/100th of a semitone.

50 cents is therefore one-half of a semitone. So, C+50 cents is the same as B-50 cents.

The equal temperament does not result in pure intervals, and is not as harmonious as just intonation.

A standard guitar is by its very nature an equal temperament instrument. The relative pitch of the notes is determined by the positioning of the frets. You cannot use Just Intonation on a standard guitar.

There are guitars made that do play in temperaments other than equal temperament. These either have more than 12 frets per octave, or have frets that are not straight. You can learn more about these instruments at the following links:

http://www.freenotemusic.com

http://www.truetemperament.com/site/index.php

I hope this has been of some help to you.