In the modern (within the last century!) era of Classical Music training, there has been an unfortunate emphasis on what is considered technical perfection. This has led to a phasing out of many centuries worth of accumulated musical skills that were used to better emphasise the rhetorical and emotional impact of music. Many of these skills are now considered mistakes or imperfections in the attempt to create a pristine marketable product.
Playing Together
One of these ideas has been the idea that we need to be constantly playing together with one voice. The idea that within a phrase, that we are always together from beginning to end is a very modern idea, and one that runs counter to the older ideas of tempo rubato.
Rubato (robbed time) in the modern classical meaning, describes the idea that the motion and playing of a phrase is fluid. Thus, at certain points you speed up and slow down depending on the music but at all times the two hands of a piano or the various parts of an ensemble are doing the speeding and slowing together.
So, we have these two examples of Debussy's 1st Arabesque, the first version without rubato (a computer version) and then a second human version where the speed ebbs and flows.
Without Rubato
With Rubato
Hopefully it is clear that the second performance had more musical meaning that then first!The mirroring of music with speech means that it makes no sense for music to march onwards in metronomic time. When we speak, our speech within sentences also ebbs and flows in speed. If you think about how stilted a robotic recording of speech can sound, the same holds true in music!
The REAL Rubato
Despite this modern notion of rubato being still central to the musical meaning of a performance, it is NOT the real original intent of rubato. Tempo rubato from the history of music (before 1940's) had always referred to the stealing of time WITH RESPECT TO the other parts. So, the "accompanying" parts had their own tempo meaning whilst the "expressive" part moved freely through the underlying structure.
It was not that the underlying parts had no expression at all, but just a different one. It was understood that the contrast in timing between the "accompanying" and "expressive" was something that brought greater meaning to the music. If all the parts spoke equally the same, then the effect of contrast would have been lost.
For comparison, here is an old recording reworked by Julius Katchen, where you notice that the left and right hands of the piano are not together, but they join up at critical points. For reference, you can hear the original recording at the beginning of the Youtube clip (it is just really really degraded!)
NOTE: I'm not sure I did the embed code right. You shoudl start at 2:00 for the modern reworking.
Contrast this with the modern day performance (still good performance), where the left and right hands are completely always in sync. It is a really different experience.
So, this has been one of the lost skills that the specialisation of Early Music has tried to rediscover and bring back into music making (see one of my orchestras, 
It is a hard thing to breed out of our modern conservatory music training, but once you have, it is a skill that opens up new vistas of expression in music making!
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