1. **Problem Statement:** We are given the set $C = \{x \in \mathbb{R} \mid -3 < x < 3\}$ and asked to understand its meaning and graph. 2. **Understanding the Set Notation:** The set $C$ includes all real numbers $x$ such that $x$ is strictly greater than $-3$ and strictly less than $3$. 3. **Inequality Explanation:** The inequalities $-3 < x < 3$ mean that $x$ can be any number between $-3$ and $3$, but not including $-3$ or $3$ themselves. 4. **Graphical Representation:** On a number line, this is shown as an open interval between $-3$ and $3$ with open circles at $-3$ and $3$ indicating these endpoints are not included. 5. **Summary:** The set $C$ represents all real numbers strictly between $-3$ and $3$. Final answer: $$C = \{x \in \mathbb{R} \mid -3 < x < 3\}$$