Peak purity is a comparison of the reference standard to the API in the sample stressed by 'forced degradation (thus specificity). In essence you are showing that no impurity (related substance) is eluting underneath the main API peak in HPLC. You are slicing this sample peak and comparing it with the API peak which is at least 100 mAU high. The comparison criteria is not less than 0.990. The threshold of the API peak is typically at 1/2 height.
Agilent has a very good description by Mark Stahl.
Purity angle: The average value of the angle between each spectrum of the peak and the spectrum at the top of the peak. In other words, the purity of the entire peak can be determined by this value.