Music is about sound and silence. The pauses in music are as important as the notes.
Technically, pitch is about frequency and the relationships of sounds. Music is composed of elements of different frequencies sounded one after the other (melody) or sounded together (harmony). When a note is sounded, it is because the instrument has been made to create a vibration - a string, a reed or a column of air typically. This vibration is passed by changes in the air to our ears where it is interpreted by the brain. That means that pitch is a subjective thing whereas frequency is a numerical measure of the number of vibrations per second.
Is the speed you play at. It is measured in beats per minute and is what a metronome indicates. Tempo varies widely for the same tune depending on where, when and on what the tune is played - also who is playing it. There is no right or wrong in traditional music, but there are some guiding ranges - usually governed (at least originally) by dancing. Thus reels and jigs can be played slowly or quickly for example, but airs should never be played quickly.
The regular pattern of a piece of music which gives the characteristic name to the type of tune - Reel, Jig, Mazurka, Waltz, etc. Each of these has a particular recurring pattern with emphasis in certain places. Waltz for example is one, 2,3 one, 2,3 etc. See Rhythms for more on this topic.
Timbre is the quality of the notes played. The difference you hear when a tune is played on a mandolin and then on a banjo is the timbre, reflecting the way the sound is produced. In technical terms, it is the shape of the waveform produced by the instrument together with the 'envelope' of sound produced. That is each instrument has a characteristic attack and decay to the note as well as the amount of sustain the instrument can produce by its construction. All plucked instruments have a very rapid attack as the string is struck and a similar release as the string stops vibrating. A wooden instrument such as a mandolin has a longer sustain than a banjo - mandolins 'ring' after a note is produced whereas banjos don't. The decay is the time from the attack to the level sustain - again similar for stringed instruments. By contrast, forcing air over reeds or down columns of air gives a slower attack, virtually no sustain (if the air is stopped) or decay and a rapid release.
The techniques of changing from one note to the next. Notes may be slurred together (legato or slur), played distinctly, separating each one (staccato) or emphasised (accented) that is played slightly louder or slightly longer.
Tempering is something you will come across in traditional music, and it is to do with the construction of certain instruments. Modern instruments are mostly made to play together - ensemble but some were made to a different temperament (older concertinas and many pipes for example). Temperament is a form of tuning which forms a compromise between the natural tones (pitches) of the instrument and the requirement to play with other instruments. The natural tuning of instruments is called just temperament. The compromise to play ensemble is most often what is called equal temperament and is one example of a series of compromise schemes called well temperament. In brief, when an instrument is made, the natural relationship between pitches is governed by the exact relationship of the frequencies produced - being fractions or multiples of the fundamental frequency (i.e. the vibrating frequency of the open string). To play in different keys would require a different fundamental and a different set of relationships. The place where the string would be stopped to sound the same interval in different keys would be slightly different. The upshot of this, is that the frets are laid out to a mathematical formula which actually slightly fudges certain notes away from the natural tuning but, if everyone agrees (which they do), then everyone playing a C# for example, will be at the same pitch. The instruments which tend to retain natural tuning are instruments which are designed to play (originally) in one key - such as bagpipes although they are manufactured these days with modern tempered intervals to allow them to play with other insruments.
Although natural scales have been used for thousands of years, it was not understood why the intervals between notes were the way they were. They just sounded right. Certain intervals sounded particularly good - the octave and the fifth but the notes inbetween were somewhat arbitrary. Pythagorus is often credited with understanding why - they were simple ratios of whole numbers which meant a lot to him. Unfortunately, from his findings, it transpired that a series of perfect fifths which ultimately brought you back to the same note but higher in frequency did not produce the same pitch as a series of octaves. There was a discrepancy. All the compromise temperings attempt to align these two series.
A series of 7 fifths returns to the starting note 4 octaves higher - but it is not exactly the same pitch as 4 octaves - there is about a quarter of a tone difference.
The reason often cited is that the fifth is a ratio of 2/3 and the octave is a ratio of 1/2 (measure it on your fretboard - the fifth is at the 7th fret and the octave is at the 12th fret) and there is no way that you can multilpy 7 lots of 2/3 and 4 lots of 1/2 and get the same number. It is perfectly possible to have an instrument that has a perfect octave and a perfect fifth, but with multiple octaves, either the octaves drift apart or the fifths drift apart (depending on whether the instrument was tuned by successive fifths or octaves) leaving a larger gap between pitches (called the pythagorean comma or wolf tone). This is what well temperament schemes sought to solve - the elimination of the gap.