I was in NY a few weeks ago and we were walking north of Union Square
(near Park and 18th I think) and I saw, on the side of a building, a
set of 13 or so large yellow numbers.  The middle most numbers were
increasing very fast while the number on either side seemed to be
ticking out seconds.  To the left and right of that digit, the numbers
were ticking slower and so on.

What is the meaning of this and what exactly do the numbers represent.

Hello,
What I believe you saw is the Metronome; it's a public artwork created
by Kristin Jones as an "investigation into the nature of time."
( http://metronome.related.com/statement.htm )

The fifteen numbers of the Metronome display time coming and going
relative to midnight. Here is an explanation that I found at (
http://www.unionsquarenyc.org/neighborhood/facts.html ):

"How to read the clock – the Metronome -- on the art wall at 1 Union
Square South? The 15 numbers of the digital clock display time going
and coming relative to midnight. Read time going left to right and
time coming in the opposite direction. So, if the clock reads
070437000235616 it means that it is 7:43 A.M. (7 hours and 43 minutes
since midnight) and that there are 16 hours, 56 minutes and 23 seconds
remaining until midnight. The three numbers in between are a blur of
moving numbers."

Here is a link to a couple of pictures of the Metronome from afar,
unfortunately you can't see the digital display from in these but this
should let you know if this is in fact what you saw.
http://www.placesofart.com/images/jones_ginzel/images_metronome/images_metronome.htm

I hope this information helps!

Helpful Links:
http://metronome.related.com/
http://www.jonesginzel.com/Metronome.html

Awesome, thanks for the quick answer.