For the reaction; $2\mathrm{HI}\to {\mathrm{H}}_2+{\mathrm{I}}_2$, the expression $-\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}$ represents:

For the reaction: 

$2\mathrm{HI}\to {\mathrm{H}}_2+{\mathrm{I}}_2$

The expression $\frac{-\mathrm{d}\left(\mathrm{HI}\right)}{2\mathrm{dt}}$ represents the instantaneous rate of the reaction.
The instantaneous rate of the reaction $=\frac{-\mathrm{d}\left(\mathrm{HI}\right)}{2\mathrm{dt}}=\frac{\mathrm{d}\left({\mathrm{H}}_2\right)}{\mathrm{dt}}=\frac{\mathrm{d}\left({\mathrm{I}}_2\right)}{\mathrm{dt}}$

Therefore, the correct option is (C).