Not being a Spanish speaker and hearing the word CADENCIA over and over again I tried to do my homework and simply google the answer. What is cadencia? You can feel it. You can see it, but when you try to find the verbal explanation it becomes extremely vague.
My intuitive understanding is that it is dancers interpretation of the phrasing of music, their response to it. Almost sort of translation. If music was a foreign language and the dancers the interpreters they can take the music and translate it into dance. Now - here in New York most people are bilingual and we all know that sometimes the word to word translation makes no sense. Or it makes sense but its ugly. The exact translation does not carry the real meaning. Looses it somehow or makes it flat. We all know that certain words and phrases mean more or mean something else than it seems at the first glance. They also mean something else when said in certain tone of voice or certain facial expression or in certain situation. So when we translate from English to our language (whatever that language might be) - we never really translate literally. However - we do try to find the way to keep rhythm and phrasing similar to original not to loose the intention of the author, the intention of the music. When the musical phrase comes to the close - the movement comes to the close.
Here is the video of the class teaching 'cadencia' explained as a sort of rocking movement.
In http://www.thefreedictionary.com/cadence cadencia is explained as - the close of a musical section
So it can be said that cadence refers to how one closes musical sequences. The movements should always illustrate, or be a variation of, the musical cadence / intonation.
At Joy in motion website we read: 'Cadencia, for me, relates very strongly to pauses and momentary lilts – part of the punctuation – of the dance, since it is in these moments when obvious movement is at a minimum and, therefore, internal energy can be felt the strongest. It feels very much like the “falling into simplicity” of musical cadence, a slow deep breath that provides both rest and a building of energy to return to action. Isn’t this how we begin the dance, letting the music and the connection fill our body like lungs fill with air, waiting for the impulse to move? And isn’t this also how we finish the dance, settling into a final position that provides release and a parting essence? The start, the finish, the pauses in between… this ebb and flow of the dance, with its peaks and valleys, is also present in my body when I execute a pause and feel that quality of cadencia coursing through my body, that “surfing on the waves of the music and the connection.” (See more at: Joy in motion)