The color data obtained from spectrophotometric measurements has no relationship to human visual assessments of color. The spectrophotometer measures the reflectance of different wavelengths of light which is a physical phenomena. It is of no value to measure color unless the measurements relate to what we see. In order to make use of spectrophotometric data in the setting of product specifications, acceptance tolerances, etc., it is necessary to first convert the spectrophotometric data to a color scale which relates to visually observed color.
1931 Standard Observer (2º Standard Observer) - how the average person saw color as a result of the 1931 CIE experiment where samples were observed via an area of approximately 2º at arms length e.g. an area the size of a U.S. quarter
1964 Standard Observer (10º Standard Observer) - how the average person saw color as a result of the 1962 CIE experiment where samples were observed via an area of approximately 10º at arms length e.g. an area the size of a softball
Since a change in observer is just a calculation in a spectrophotometer, after the sample is measured, color values for different observers can be determined with just a click of a button. It is important to understand, though, that color values obtained under one observer will be different than those obtained under a different observer, This is because the size of the area being viewed does have an effect on how people see color.
In general, if illuminant C is used the observer is normally 2º. Likewise, if standard illuminant D65 is used the observer is normally 10º.