Once a structure solution has been achieved, either by Heavy Atom Methods or Direct Methods, there are actually two structure models, a calculated model based on the approximate co-ordinates obtained from interpretation of a three dimensional electron density map:

and an observed model based on the calculation of structure factors from experimental intensities: Below is the beginning of the first page of the structure factor tables for a 38 atom organic molecule (this table continues for a total of ten pages for a total of 4473 reflections):


The F tables list 10F_o (ten times the observed structure factor), 10F_c (ten times the calculated structure factor) and 10s; (ten times the standard deviation of the observed structure factor).
The task now is to adjust the various atomic parameters so that the calculated structure factors match the observed structure factors as closely as possible. One of the ways to measure the agreement between the observed and calculated models is with the Residual Index (more commonly referred to as the R-factor):

(At the present time, most small molecule crystallographers refine on F² rather than on F, but this discussion will be based on F - it makes the notation a little simpler. For a discussion focusing on why refinement should be on F², go here).