To determine which of the given expressions represents a fraction, we analyze each option based on the presence of unknown variables in the denominator:

- For option $A$, $\frac{x}{2}$, the denominator is $2$, which is a constant and does not contain any unknown variables. This means the expression is a polynomial, not a fraction in the context of this question. Thus, $A$ is incorrect.

- For option $B$, $\frac{x}{\pi}$, the denominator is $\pi$, which is also a constant and does not contain any unknown variables. Similar to option $A$, this means the expression is a polynomial. Therefore, $B$ is incorrect.

- For option $C$, $\frac{x}{x+1}$, the denominator is $x+1$, which contains an unknown variable $x$. This means the expression has a variable in the denominator, classifying it as a fraction in the context of this question. Thus, $C$ is correct.

- For option $D$, $\frac{x}{2}+y$, the denominator of the fraction part is $2$, which is a constant, and adding $y$ does not change the fact that the fraction part $\frac{x}{2}$ is a polynomial. Therefore, $D$ is incorrect.

Based on the analysis, the expression that represents a fraction, due to the presence of an unknown variable in the denominator, is option $C$: $\frac{x}{x+1}$.

Therefore, the correct answer is $\boxed{C}$.