What is the intuitive meaning of outer product in Hilbert space

Question

What is the intuitive meaning of outer product of $|\psi\rangle\langle\psi |$ in Hilbert space?

Answer 1

It is the projection operator of some state $|\phi\!\!>$ onto $|\psi\!\!>$.

For example, if $|\psi\!\!>$ is a state of some definite momentum $p$, and $|\phi\!\!>$ some state of uncertain momentum and position, then $|\psi\!\!><\!\!\psi| \phi\!\!>$ selects the momentum = $p$ component of $|\phi\!\!>$.