Originally Posted by: pizzicatopickerwhat is a Cadence[/quote]
A cadence is the ending of a harmonic progression. Ending a phrase on a five chord is a half cadence; ending on a one chord is a full cadence. There are further disticntions. Wikipedia is frequently a good source for defintions:
http://en.wikipedia.org/wiki/Cadence_%28music%29

From complex classical melodies, themes down to traditional nursery rhymes the idea of a cadence is crucial. From Beethoven's sym. 9 the "Ode To Joy" theme, the first phrase is the "question phrase" and ends on a five chord and is thus a half candence:

E|-0----1--3--|-3--1--0-----|---------0--|-0--------|
B|------------|----------3--|-1----3-----|------3---|
G|-0----------|-------------|------------|-0----0---|
D|------------|-0-----0-----|-2----------|----------|
A|-3----------|-2-----------|-3----------|-3----2---|
E|------------|-------3-----|------------|----------|
I V I I V

Then, the "answer phrase" ends on a I and is thus a full or "authentic" cadence.

E|-0----1--3--|-3--1--0-----|---------0--|-----------|
B|------------|----------3--|-1----3-----|-3----1----|
G|-0----------|-------------|------------|-----------|
D|------------|-0-----0-----|-2----------|-3----2----|
A|-3----------|-2-----------|-3----------|------3----|
E|------------|-------3-----|------------|-3---------|
I V I V I


Originally Posted by: pizzicatopickerA leading tone[/quote]
http://en.wikipedia.org/wiki/Leading-tone

Usually the leading tone is the major 7th note of a scale. It "leads" the ear to the one or root of the scale. But the flat 2 (a half step above the root instead of below) can also be used as a leading tone. Especially in jazz - tritone substitution http://en.wikipedia.org/wiki/Tritone_substitution and certain classical-romantic styles - Neapolitan sixth http://en.wikipedia.org/wiki/Neapolitan_sixth and the augmented 6th http://en.wikipedia.org/wiki/Augmented_sixth_chord .

Before you think that's "way too complicated" :p. Consider that you've heard it a million times in blues songs that end with a big flat 2 chord - as a substitution for the five - then a 1 root chord. Or in metal songs that use the flat 5 and flat 2 chord all over the place. These are very simple straightforward examples of using tritone subs, augmented 6ths and Neapolitan chords.
[QUOTE=pizzicatopicker], and, especailly, what is the difference between a scale and a [U]mode[/U]?

A scale is a series of notes spaced at specific intervals between an octave. A mode is using each note of a scale as it's own temporary "root" or reference point.

So a scale is more fundamental. Here's an analogy: Different scales are completely different objects. A mode is merely a different perspective on the same object (the scale you are making modes out of). Modes are derived from scales.
http://en.wikipedia.org/wiki/Musical_scale
http://en.wikipedia.org/wiki/Musical_mode
[QUOTE=pizzicatopicker]I'm not frustrated at all, becuase I really want an understanding of theory, because, after all, it's beyond important; It's essential.

Great attitude. :) Hope these answers help.