It has mostly to do with being very out of touch with your own emotions, being unable to describe your emotions if asked, being unable to tell what exactly is causing your emotions and why, and so forth. The way I understand it, it basically means you are extremely disconnected from your own emotions and generally emotionally stunted because at some point you "shut down" your emotions as a defense mechanism. And since you're really out of touch with your own emotions you have problems with emotionally relating to others because you are kind of emotionally "dumb" and emotionally disconnected, which makes non-superficial relationships very hard.
I can definitely relate to the ones you pointed out, Hoasis, but honestly I can related to pretty much all of it... seems like it could be one pathway to AvPD but I'm sure there are others and that not everybody here can relate to it. Maybe some AvPDers can describe their emotions really well and are "in touch with their feelings" but I am the total opposite and couldn't articulately express my emotions to someone else to save my life. And it doesn't mean you have NO emotions or that you cannot express them in a rudimentary way, but you might use overly simplistic words like "upset", "down", "happy", etc. instead of being able to paint an appropriately complex and differentiated emotional world that an emotionally "healthy" person would feel and be able to describe.
It overlaps with a lot of mental disorders, not just AvPD. People with Schizoid, Borderline, Avoidant and Antisocial PDs are more often alexithymic than the general population but it is associated with many non-PD mental disorders like autism spectrum disorders, PTSD, anorexia/bulimia, major depression, and social phobia as well as substance abuse.
I don't think you can trust these things very much but here is the online alexithymia questionnaire if anyone is interested. My main complaint with it is that I couldn't relate at all to the questions about relying on other people to interpret how you should feel in a situation because I mostly just avoid people let alone emotional conversations, heh. Don't think those questions have high validity for avoidants so I just picked undecided for them:
Online Alexithymia Questionnaire