An entity born of the will of the town, Pyramid Head's personality is a stunted, warped thing mostly lost beneath his purpose. He is driven to seek out and punish those judged as guilty, either by the town or by themselves, and to carry out the appropriate punishment. This may manifest in either straightforward violence, as with the execution of Alex's father in Homecoming, or the more sexual nature of his assaults in Silent Hill 2 toward the feminine monsters of James' subconscious. His exact role is determined by what the town, and the subconscious of whoever is currently influencing it, wills--something which may account for his differing garb and weapon in his various appearances with different characters.

He does not pause to question his role, carrying out his tasks with the frightening directness of something which feels no compassion or mercy. He is, quite basically, a monster. He exists only to obey his creators and their will, and everything else is simply inconsequential. Pyramid Head is mostly a threat to those who are overwhelmed by guilt or feel an intense need for punishment, although he will lash out at anyone who catches his attention, but innocents who are otherwise not affected by the same darkness that drags others into the Otherworld slip entirely past his radar and are, more or less, safe from him.

Basically he's a terrible thing created to carry out horrible punishments on those who are unfortunate enough to catch his notice, with no concept of right and wrong beyond what has been established by the cult and their gods. Violent and singleminded, he's used to a lack of autonomy created by the town speaking to him--he has had no reason to ever think or do anything beyond the purpose he was created for.

In the games, Pyramid Head is portrayed as an unstoppable force, able to soak up damage without hesitation or any indication of pain, and is essentially unkillable if not invincible. This will change in Singularity.

Much like a zombie, decapitation or destruction of the head/brain, or sufficient dismemberment, will kill Pyramid Head, and damage inflicted on his body will actually show up as... real damage. Rather than be invincible as he was before, he will heal at an unnatural rate if he is not outright killed (something like twice the normal speed, not an insta-heal).

Aside from that, Pyramid Head is quite strong and has a relationship to pain that makes it anything but an issue for him.

For weaknesses, it must be said that he's rather slow. The weight of his helm and the great knife drags him down, making him a methodical, lumbering adversary most of the time, with only a few short bursts of speed. Additionally, while his head is fairly well-protected by the helm, the rest of his body is completely unarmored and he makes no attempt to defend himself from any wounds. Things such as protective wards and similar things will slow him down or turn him away due to the strong magic/mythos influence in the Silent Hill world.