$$\sum {| n \rangle \langle n |} = 1\\
\sum {| n \rangle \langle n | \psi \rangle} = | \psi \rangle$$
This represents the expansion of ##|\psi\rangle## into a linear combination of orthonormal basis states ##|n\rangle##. The ##\langle n | \psi \rangle## are the coefficients of the expansion. In the position representation we usually write this as something like