I'll put my head on the block and try to answer this one
Also, I'm assuming we're talking about the relationship between music and dancing, not just about music. Rhythm is the most difficult, so I'll leave that till last
***Timing***
This usually refers to being on the beat, dancing at the correct speed, and starting figures at the appropriate beat of the bar. So when someone says “dancing out of time” they usually mean either or both of “dancing too fast/slow” or as an example “starting a waltz natural turn on beat 2 instead of 1”
***phrase**
A phrase in the music refers to a segment of the music (usually 4 or 8 bars) which ‘makes a statement' For example, the song ‘True Love'
(I) Give..to
You… and you
Give…..to
Me
(((end of first 4 bars - each line is a bar))))
True
Love
True
Love…….and
((((end of second 4 bars)))))
and so on.
Good phrasing means interpreting these ‘segments' (i.e. bars) in a way which seems good and looks good (‘good' is hard to define here – it's all about artistic interpretation of course.
******Rhythm*****
Difficult to define. Here's something..
The rhythm of a piece of music depends on several things – the tempo at which it's played, the ‘repetition' of certain accents (e.g. beats in the bar, but more than that) and syncopation (accenting notes not on the beats). there may be 2 or more interlocking rhythms as well (think of bolero where the melody line is simple, but the accompaniment is more complex – pity the poor drummer!).
How does rhythm affect dancing?. Well, lots of music is 4 beats to the bar, but the different ‘rhythm' - accenting and tempo - make some of it foxtrot music, some of it rhumba, cha-cha, quickstep, and so on.
Ok someone else have a go