What is Phase problem, R factor?

The intensities give $|F_{hkl}|$ but not the phases of the $F_{hkl}$; without them the electron density cannot be computed by inverting the Fourier series. This is the phase problem. A trial structure is refined by least squares until computed and observed moduli agree; the residual $R = \sum\big||F_o| - |F_c|\big|/\sum|F_o|$ is its R factor — a few per cent for a good structure.