The zero-th moment $\langle 1\rangle$ is just the normalization condition of $p$. The first moment, $\langle x\rangle$, is called the mean of $p$ and often denoted by the letter $\mu$ $$\begin{equation*} \langle x\rangle = \mu \equiv \int x p(x)dx, \end{equation*}$$ for a continuous distribution and $$\begin{equation*} \langle x\rangle = \mu \equiv \sum_{i=1}^N x_i p(x_i), \end{equation*}$$ for a discrete distribution. Qualitatively it represents the centroid or the average value of the PDF and is therefore simply called the expectation value of $p(x)$.