Headmasters are the early prototypes of a process known as binary bonding, in which a Transformer and another being are able to share their thoughts and sensations through an almost psychic link. In the case of a Headmaster, this other being is able to actually transform into the larger Transformer's head, usually replacing the original head - which is removed as part of the initial process. Although usually this bond is to a Nebulan, the species who invented the procedure, some Transformers have been known to bond with humans, Mini-Cons, and even other Autobots or Decepticons.
History
The first and original intent of the Headmaster process was to allow a Nebulan to control the body of a Transformer. This was initially done as a kind of enslavement, overcoming Nebulan distrust by forcing Autobots to give up their heads and placing them completely under the power of their Nebulan partners (hence the term Headmaster). Since the Headmaster partner can provide all of the motivation for a Transformer body to move and fight without the Transformer even needing to be conscious (or alive), and can override the will of the Transformer he or she is bonded to, many Autobots and Decepticons find this technology disturbing. There are, however, many benefits to the procedure - enough so that after facing Autobot Headmasters in combat, the Decepticons realised that they needed to take advantage of this technology as well. Although the initial partners were Nebulans, several humans were also involved in this process, including (in some continuities) both Daniel Witwicky and Spike Witwicky.
Headmaster partners are unique amongst their brethren (the Targetmasters and Powermasters) in that they have the power to take full control over the body they are connected to, often against that Transformer's will. However, over time, both the Headmasters and their Transformer partners realised that they worked better when both sides had a say in things (two heads being better than one), and the relationship between them evolved from master/slave into a more equal partnership. In that cooperation lies the real strenght of the Headmaster process.
In Japanese continuities Headmasters hail from the planet Master and generally used Transtectors, robotic bodies that were devoid of sparks and non-sentient(therefore avoiding the messy argument over whether Headmastering was ethical by not partnering with living Transformers). A Headmaster is born when one of the miniture denizens of Master (Roughly a little bit larger than a human, save for Scorponok) proves his worth in combat, and is rewarded with his very own Transtector, in order to be able to fight more efficiently among the Master's larger brethren. These Headmasters have the ability to use another Headmaster's Transecters in order to utilize new powers (This is a nod to the Headmaster's toys who had Tech Specs meters that changed depending on what Headmaster was used).
Terminology
In conversation, the term "Headmaster" can apply to both the primary partner (the head), and their significant other (the body). To be called a "Headmaster", a Transformer needs to have an autonomous partner who changes into their head as part of their transformation sequence. The benefits of this procedure are many: the partner gains control of a larger, more powerful body, and the Transformer gains an extra perspective on the battlefield, being able to draw on both his own ideas, tactics, and instincts as well as those of his partner as quickly as if they were coming from his own head (since they are).
Technology
A mini-con or fellow Transformer, of course, has no problem changing their form into that of someone else's head, but organic partners need a little help in pulling it off. Human and Nebulan Headmasters do this by use of a special suit of Headmaster armour as well as (in comic continuity) surgical bio-cybernetic augmentation. Sometimes the Headmaster armor is not unlike an Exo-suit, transforming around the wearer (G1 Cartoon). Other times it is larger and almost a mecha of its own (DW Comics). Other times is appears to be just an outer layer of Cybertronian armor and the actual mechanics of being a Headmaster and transforming is surgically created inside the partner, transforming them into a cyborg who interfaces with the armor (Marvel Comics). Headmaster armour can be passed on to other people in an emergency, or in the result of a Headmaster's death. The helmet seems to be the most important part of the overall design, creating the mental link, since Spike Witwicky has shown himself able to command the body of Fortress Maximus while wearing only that one part, but the entire suit (and in the comic the surgical augmentation) is needed to transform oneself into the head and take full control.
It has been shown as well that while connected to a Transformer, a Headmaster partner can use their form as an extended kind of advanced life support - at least one Headmaster (Arcee) volunteered for the process in order to save the life of a human ally who had been severely wounded in battle.
Without their head, a Transformer Headmaster is at a severe disadvantage. Most Autobots and Decepticons are shown entering a kind of stasis lock when their heads disconnect from their robot modes, often seeming sluggish and able to perform only the most basic of functions. In their alternate modes, however, a Headmaster seems no different from any other Transformer: if, perhaps, a little more dangerous. With another intelligent being to help with the task of driving, flying, or shooting, the Headmaster is able to focus more clearly on tactics, strategy, or just the task at hand, freeing up considerable processing power from more mundane requirements. This makes a Headmaster capable of extreme multi-tasking and amazingly rapid decision-making, if the two partners have similar attitudes and mindsets.
Flaws
The main weakness in the design comes from conflicts of personality. Since there was never meant to be an equal partnership in the original Headmaster concept, very little attention was paid to how the Transformer and their partner would interact during the original bonding. As the prototypes of the binary bonding idea, the Headmasters suffered from a lack of knowledge on how important this interaction would be. Many early Headmasters simply did not get along with their own bodies, and vice-versa. Because of this, partners would often disagree or be at odds with each other, resulting in confusion in the Transformer as the voices in his head had extended arguments over what to do. Depending on the compatibility and personalities of the partners their minds tend to merge to different extents and their joint psyche manifests in unique ways for each individual. (For instance, in the comic, Spike and Fort Max were two separate minds sharring one body, with each dominant in their own form and the other submissive, while Lord Zarak and Scorponok seemed to reach some sort of fusion where he was both beings merged into one.)
(Note: this was not an unexpected problem for the Transformers. Early combiner teams had similar issues, with the resulting gestalt being much simpler and less intelligent than the sum of its parts, often because the parts did not get along. However, since the Nebulans failed to ask before starting the Headmaster plan, they were not able to avoid this problem)
Also, the transformation of most Headmasters seems to prohibit regular movement, but of course this is often a problem with G1 toys.