Tony, this is going to look like I'm picking on you in particular here, but I'm really talking about this kind of comment in general.
Your comment is not really helpful.
Its the kind of thing written by someone who has no appetite or desire for music theory or a deeper understanding of the instrument.
Just the opposite. Sounds to me like a man who's been around that block and arrived back at himself again.
Knowledge (theory) is not understanding. Deeper understanding can be when you realise that notation doesn't mean S*it and you still need to play something appropriate to what you're hearing and make it feel and sound good. That's the beginning, middle and end of it. The thing is, you need to have studied theory thoroughly and truly grasped its monumental limitations to arrive at that place.
Theory is a road map, not to be mistaken for the actual landscape or the journey itself.
As to the topic - time signatures are attempts to codify sound in visual form. Played music preceded written music.
3/4 is an attempt to codify a pulse of three beats divided primarily into duple subdivisions.
6/8 is an attempt to codify EITHER a pulse of 6 beats or, more commonly, a pulse of 2 beats divided into triple meter.
And the most effective way to demonstrate this to a student is always to play examples of both. That is, you go back to sound and feel to give the theory meaning.
One of the tunes I use to help my students understand this is
America from
West Side Story. Of course, there Bernstein wrote mostly in 6/8 with the "3" bars being hemiola in 6, but the effect is the same:
http://www.youtube.com/watch?v=Qy6wo2wpT2k&feature=kp
That said, just to show the pliability of theory/time signatures, you could just as easily write the two first bars of the melody as a bar of 4/4 and a bar of 2/4 so that the accents in the first bar land on 1, the and of 2 and 4 and then on 1 and 2 of the second bar. Bar lines are partly to indicate where strong pulses should be felt (i.e. beat 1) but in another way they're quite arbitrary and in large part simply to divide the visual presentation of sound into even units so as to make it easier to digest, learn and rehearse. There was a time when music was written without bar lines.
(Aside, but germane: some of the swing stuff in WSS was originally written in 6/8 instead of in 4 with triplets. Makes it a trip to read if you're used to the usual presentation. The real trick is to stop reading and trying to think the time signature and
hear it.)