%matplotlib inline is an interactive Python  (iPython) 'magic command' used when running Python within a Jupyter notebook. It allows the display of data plots within the notebook. 

Tip: When running Jupyter notebooks within Authorea , the%matplotlib inline command must precede the from matplotlib import pyplot command. 

plt.figure() signifies the beginning of the plotting instructions specific to that figure.  

plt.errorbar(angle, V_pd, xerr = None, yerr=V_pd_delta)  is the command that instructs matplotlib to generate a x-y plot with error bars (as opposed to a bar graph or scatter plot, for example).  All four parameters (x, y, xerr, yerr) are required.

linestyle and color are used to customize the appearance of the data points. Linestyle = None means there are no connecting lines between points. Color means the color of the error bar lines and caps. The standard colors are blue, green, red, cyan, magenta, yellow, black, and white (with corresponding abbreviations 'b', 'g', 'r', 'c', 'm', 'y', 'k', and 'w'). 

capsize, and capthick are  used to customize the appearance of the error bars.     capsize =3 sets the width of the error bars to '3' (in typesetter points), and  capthick=1sets the thickness of the drawn bars to '1' (again in typesetter points). Note that if  the  capsize and capthick commands are omitted,  matplotlib will draw  lines indicating the given uncertainty but will omit the bars! 

plt.show() signifies the end of the plotting instructions and causes matplotlib to plot the data.