Most polymers are semi-crystalline, meaning they have regions where the polymer is crystalline and regions where the polymer is amorphous. In crystalline regions, the polymer strands line up in regular, highly ordered ways. In amorphous regions, there is no long range order. Crystalline regions tend to be dense, strong, and rigid, whereas amorphous regions are porous. The crystalline phase fraction, more usually called just the % crystallinity, is the fraction of the polymer that is crystalline (usually by weight). So a polymer with phase fraction of 0.5 has 50% of its weight in crystalline phase and 50% of its weight in amorphous phase. The phase fraction affects the bulk properties quite a bit. It is the main reason why high density polyethylene is higher density, stronger, and less porous (better barrier to diffusion) than low density polyethylene. The amount of polymer branching, often influenced by the catalyst one uses during synthesis, affects the phase fraction because more branched polymers are less able to form crystalline regions. Crystallinity is also influenced a lot by how the polymer is processed, chiefly the cooling rate, and also any additives present. So for a polymer manufacturer it's an important quantity to control and measure.
% crystallinity can be determined in a lot of ways, but most frequently by discrete scanning calorimetry (DSC) and x-ray diffraction (XRD). Here it looks like they are using FTIR. All of these methods work because crystalline regions have different thermal, spectroscopic, or particle scattering properties than amorphous regions.