From Szabo Ostlund 'Modern Quantum Chemistry'

Given a normalized wavefunction of N-electron system $\Phi(\mathbf{x_{1}},...,\mathbf{x_{n}})$, then $\Phi(\mathbf{x_{1}},...,\mathbf{x_{n}})\Phi^{*}(\mathbf{x_{1}},...,\mathbf{x_{n}}) d\mathbf{x_{1}}...d\mathbf{x_{n}}$ is the probability that an electron is in the space-spin volume element $d\mathbf{x_{1}}$ located at $\mathbf{x_{1}}$, while simultaneously another electrons in $d\mathbf{x_{2}}$ located at $\mathbf{x_{2}}$ and so on. If we are intersted only in the probability of finding an electron in $d\mathbf{x_{1}}$ at $\mathbf{x_{1}}$ independent of where the other electrons are, then we must average over all space-spin coordinates of the other electrons, i.e. integrate over $\mathbf{x_{2}},...,\mathbf{x_{N}}$ to obtain $$\rho(\mathbf{x_{1}})=N\int d\mathbf{x_{2}}...d\mathbf{x_{N}} \Phi(\mathbf{x_{1}},...,\mathbf{x_{N}})\Phi^{*}(\mathbf{x_{1}},...,\mathbf{x_{N}}) \quad (Eq.1)$$
where $\rho(\mathbf{x_{1}})$ is called the reduced density function for a single electron in an N-electron system.

I still dont quite understand the meaing of (Eq.1). $\int d\mathbf{x_{1}} |\Phi(\mathbf{x_{1}})|^{2}$ can be interpreted as integral of the charge density at $\mathbf{x_{1}} $ which is the number of electrons at $\mathbf{x_{1}} $. So I think $\int d\mathbf{x_{2}}...d\mathbf{x_{N}} \Phi(\mathbf{x_{1}},...,\mathbf{x_{N}})\Phi^{*}(\mathbf{x_{1}},...,\mathbf{x_{N}})$ is the total number of electrons at $(\mathbf{x_{2}},...,\mathbf{x_{N}})$ as function of $\mathbf{x_{1}}$ and i cant see how my intepretation is connected to the probability of independently finding an electron in $d\mathbf{x_{1}}$ at $\mathbf{x_{1}}$.