
Character: tweetfur
An anthropomorphic representation of the Twitter bird, originating as a joke based on Twitter's terms and service regarding their logo, one point of which specifies "don't anthropomorphize the logo". Created in this tweet.
In reality, "anthropomorphize" has a double-meaning; what the guideline has a problem with is websites customizing and stylizing their social media links, often adding cartoon features to the logo — something seen as tacky, distracting, and unprofessional, but was common early in the site's history. Numerous examples of this can be seen here. Twitter doesn't actually have any problem with the other sense of "anthropomorphize", so no user has gotten in trouble for drawing and posting Tweetfur. If it was used as the artist's primary social media link, though, then it would be a different story.
Interestingly, the Twitter Bird's original name was "Larry", though this name has long been out of use, the logo now being nameless.
Twitter was created on 2006-03-21, which means that Tweetfur is 17 years old as of writing (and was 12, nearly 13, when the trend started).
This tag implicates twitter, meme (learn more).