I've only recently been using this Illustrator feature, but I've found it to be very useful for really precise drawing. In my case, when I draw fonts. I want to show you how to use the Illustrator “Average” feature to get perfect point alignment during drawing.
As you can see in the image above, I have two pieces of a lowercase “f” that I want to merge together with pathfinder. Below I have the two pieces lined up where I want them, and If I simply use pathfinder now and merge them, I will get more than one point on the bottom left curve, where the arrow is. I want to have a nice clean curve there, so I'm going to use the “Average” function.
As you can see here, in wireframe mode zoomed way in, the 2 points are not exactly lined up.
As pictured above, use the Direct Select Tool (white arrow) and select the 2 points you want to align.
Go to Object > Path > Average, and select “both,” then hit ok.
And that's it. Now your points are in exactly the same x,y coordinates, so when you use pathfinder, the result is only a single point, not two.
Now I have my nice clean path outline to work with!