Being socially awkward means that you lack the basic social skills that are deemed to be normal. Skills like making eye contact and holding a conversation just to name a couple. Things that would help you fit in. The image used on these memes are of a penguin captioned with some of the typical antics that someone who isn't comfortable in a social setting who deal with like going in for a side hug when the appropriate greeting is a side hug and not having a clue how to react to a friend's show of emotion. These are just a couple of examples of the type of socially awkward penguin meme you will find here.
If you are not a person that feels the most comfortable socializing or have a friend that fits this description you will definitely find a meme in this section that you can relate to.