Basically, if you omit the $ symbol in the formula, the cell references will change when you copy it down. As coded, copying gives:
{=SUM(IF(C3=C$1:C$500,1,))}
{=SUM(IF(C4=C$1:C$500,1,))}
{=SUM(IF(C5=C$1:C$500,1,))}
and so on. Without the $ you'd get:
{=SUM(IF(C3=C1:C500,1,))}
{=SUM(IF(C4=C2:C501,1,))}
{=SUM(IF(C5=C3:C502,1,))}
and this would compromise the formula's validity for what you're trying to achieve.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]