Memetically popularized via 4chan and similar sites. An anonymous poster is a poster who uses neither a name nor a tripcode to identify themselves on tgchan's various image boards.
It's traditional for quest authors to use a name and tripcode when posting their quests; this is done to make it easier to identify which posts are the author's, even if the author's IP changes. However, despite this, there are a few of quests that have anonymous authors; these authors' posts are typically identified by their IP code and their drawing style.
For a list of quests with anonymous authors, see Category:Articles without quest authors credited.