Title text: The nice thing about headcannnons is that it's really easy to get other people to believe in them.
In fiction, "canon" describes the set of works about a fictional universe that are collectively recognized as having authenticity or being "official". These works collectively define the fictional universe. Other works may be written about fictional universes which are "non-canonical" or "apocrypha". Generally, works created or authorized by the original author(s) or creator(s) of a fictional universe are considered canon while works by others may be considered apocrypha. In other cases, the medium may be a determining factor (e.g. novels or reference books set in a fictional universe which originates in a television show or film may not be considered canon, although these are often also not created by the creators of the show or film). In some cases, the manner in which canonical works are distinguished from apocrypha is not universally agreed among a fanbase. A fiction's canon may be defined by the creators themselves, or determined by fans.
An example is Star Trek canon: Most fans agree that the five live-action television series and ongoing series of feature films (including those produced after the death of the original series' creator) are considered canon, while a plethora of novels and reference books are considered apocrypha. The short-lived Star Trek: The Animated Series is not universally agreed-upon. Some fictional universes have "levels" of canon such as Star Wars canon.
Fans often develop their own ideas about a fictional universe that are not actually part of the canon. Sometimes these are larger concepts that have gone unspoken and are presumed or agreed upon among the body of fans. In other cases, individual fans make presumptions or invent their own stories or ideas about the fictional universe. These are both examples of "headcanon". This form of pseudo-"canon" exists only in the mind of the fan watching or reading the material. That fan experiences the material with a certain additional backstory or certain elements of headcanon that other fans may not. Future works may confirm headcanon as actual canon, while other headcanon may turn out to conflict with subsequently introduced canon.
Some examples of headcanon involve relationships between characters, abilities, backstories, events following the conclusion of the work, etc. which the author or creator has not explained or included. In certain cases, headcanon may become so ingrained in a fandom that a subsequent work of canon may adopt the headcanon of a fanbase. In cases where a subsequent work of canon conflicts with that headcanon, fans may be angered, even though the headcanon was never an official part of the fictional universe.
As an example of headcanon, we may return to the Star Trek universe: The character Quark runs a bar on Star Trek: Deep Space Nine. It is canonical that Quark runs the bar and that the crew of the titular space station often patronize the bar. Fans might wonder why, on a station that has "replicators" (devices that can create any food or drink out of energy on demand), anyone would patronize a bar. If an individual or group of fans created and presumed a backstory that, for example, Quark has access to replicator patterns for exotic food or drink which aren't programmed into standard replicators, or actual exotic food or drinks which cannot be replicated, that would be headcanon since the theory was developed without input or sanction from Star Trek's creators. Were the series still running, a future episiode might confirm or contradict that headcanon.
 The comic
This strip uses a play on the homophonic relationship between "canon", as above, and "cannon", a projectile weapon. In this strip, Black Hat starts to introduce a "new headcannon" (noting the spelling). Cueball, thinking Black Hat means "headcanon", inquires what Black Hat's new idea is. Instead of the expected idea or theory about a fictional universe, Black Hat removes his hat to reveal a tiny literal cannon on his head which blows away Cueball and his computer desk.
While headcanon may often be ignored or dismissed as non-canon or a personal theory, a headcannon would be far harder to ignore, as it is a physical object which has a notable (and in this case violent) impact on the real world. Randall appears to address both homophones in the title text by putting three consecutive "n"s in "headcannnon". That he uses all three "n"'s from the two words indicates that he also means that it is easy to make people believe in a self invented headcanons - this may be the actual punch-line of the comic, since it has proved very true with many fan-generated theories.
This comic also shows Cueball being once again distracted from his work in a manner similar to 1388: Subduction License.
- [Black Hat walks in.]
- Black Hat: New headcannon:
- [Cueball is sitting at his desk, using his computer.]
- Cueball: Yeah?
- [Black Hat lifts his hat, revealing his "headcannon": a tiny cannon on the top of his head. The headcannon fires and blows up Cueball's desk, the explosion throwing Cueball backwards.]
- Headcannon: BOOM
- Cueball: AUGH!