The leading note is the functional name for the seventh note of the diatonic scale. It is so called because it 'leads' upwards by semitone to the tonic.
The leading note is particularly important in modulations around the circle of fifths. If you want to modulate, for example, from C major to G major you add the leading note of the new key to the key signature (C major = 0 sharps; G major = F#, which is the leading note of this scale).
(more about the circle of fifths)
Here is a summary of the other relative and absolute note names:
There are two basic ways of labelling notes, depending on what information you want to convey. There are absolute note names such as F#1 that will always refer to the same pitch but there are also relative note names that tell you the function of a particular note within a scale or key.
Relative note names
These are useful when you want to convey the function of a note. In the example below, the simplest system is shown above the stave. Each note or degree of the diatonic scale is numbered, so in C major C is 1, D is 2 etc. - each note has a caret ^ above the number to show that it is a scale degree as opposed to, for example, a bar number.
Below the stave is the most commonly taught system, in which each degree of the scale is given a functional name (these can be used for triads as well). These names reveal the way in which different notes in the tonal system are considered more and less important.
You will notice that most of the names give the position of the note relative to either the first or fifth scale degree (mediant, for example, refers to the fact that this note is half-way between the first and fifth scale degrees). This is because the tonic and dominant have a special function in tonal music (see the introduction to tonality for more on how tonality works)
Absolute note names
There are several competing systems and you should use whatever convention your institution prefers. The following is used on this web site (as an example, an E on the first line of the treble clef is called e1):