Socially Awkward Penguin is an advice animal -- a series of internet images featuring an animal (in this case a penguin) with a short sentence or two that is in some way amusing. While the original Advice Dog did give (bad) advice, most of these types of macros do not actually give advice. While Socially Awkward Penguin is one of the more popular advice animal, you may be more familiar with Philosoraptor or Hipster Kitty.
As with the majority of the advice animals, Penguin has a color wheel background, in this case in various shades of blue. The penguin in question is an Adelie Penguin, walking with its wings spread wide and head high, with a slightly alarmed expression on its face.
The Penguin covers a wide range -- from normal teenage anxiety to 'cute' social observations to introversion to serious social anxiety. However, the most popular of the Penguin macros fall into the category milquetoast observations of slight social awkwardness. Here are some examples:
"Didn't hear what they said -- Smile and hope it wasn't a question."
"Someone bumps into you -- Apologize."
"Happy birthday -- You too!"
"Call someone -- Relieved to get voicemail."
"Dance like a manic in your car -- Stand against the wall with your drink at the club."
"Say goodbye -- Start walking in same direction"
"Doesn't know anyone at party -- Plays with dog."
"Want to cross arms -- Person I'm talking to already has their arms crossed."
"Walmart greeter didn't see me -- Safe!"
"Friend shows you Socially Awkward Penguin -- says it reminds them of you."
Socially Awkward Penguin has become so popular that it has been mirrored by a nemesis, Socially Awesome Penguin. Socially Awesome Penguin is the same penguin, but facing the other direction and on a red background. It can do no wrong, and alternates between mastering the social sphere and actively embarrassing Socially Awkward Penguin. Recently it has been common to have a split macro, with the top being Awesome Penguin (something really good happens) and the bottom being Awkward Penguin (situation is ruined by awkwardness). Because the penguins are facing different directions, these are ugly and disjointed, but that's not really the point.
Occasionally Socially Average Penguin (same penguin, green background) makes an appearance, but usually only in order to be contrasted to the other penguins. Average penguin rarely appears except in threads already populated by penguins.
Because internet memesters tend not to be very precise or consistent, Socially Awkward Penguin often overlaps thematically with Paranoid Parrot and Anxiety Cat.