They say that the reason ghosts exists is because they have unfinished business in the living world. That they can't cross over until that business is complete. The truth is a little more complicated than that. First it must be understood that only magical people, people with magical potential and those touched by magic can leave a ghost behind to complete their unfinished business. The second thing to understand is that a ghost has nothing to do with the soul of the individual because a soul cannot be separated unless it has been purposely divided and that can only happen in ways that are truly vile and evil. A ghost is actually a magical construct; in the case of most ghosts who were once magical it is actually their magical core existing in the living plain without a body to anchor and direct it. A better way to describe a ghost is as a burst of accidental magic that occurs at the time of death giving a person's magic one last duty before the body passes on. In an attempt to accomplish that duty, a ghost is formed. Poltergeists are formed in a similar fashion except that instead of wanting to accomplish specific duty, poltergeists are the magical formation of a person's last emotion.
Naturally the stronger the magic the more powerful the ghost or poltergeist. However, due to nature of their creation, a ghost's "power" is only manifested in how much they can interact with the world around them. A very strong wizard that has a very strong duty will leave a ghost that will be almost fully corporeal and who can speak and exchange ideas in pursuit of fulfilling their last duty. The more powerful the remaining magical core the more seemingly independent the spirit will be, but all things the spirit does will be in support of fulfilling their duty.
The ghosts that inhabit Hogwarts School of Witchcraft and Wizardry are particularly interesting to this study. First, it is clear that all of them were very powerful magicals, as all of them seem particularly independent in thought and action. It has been believed by some that their independence is a result of the highly magical nature of the school feeding them. That has been disproven as there are ghost in residence that are quite week and in most cases incorporeal. The poltergeist that moves the stairs is an example. That spirit has one duty and is absolutely unaware of where it is or why it moves the stairs and it is only tradition that prevents the school officials from dispelling him.
The most interesting thing about these spirits is that they do not have the ability to perform magic in the traditional sense. As in the case of the Hogwarts Stair Poltergeist, they can inhabit and affect the physical world to any degree their duty requires and the magical core that makes them up can accomplish but the can create and direct spells. The closest recorded ability discovered is that a ghosts presence can allow a non-magical being to brew potions because the potions require the presence of a magical core to catalyze the ingredients into the expected potions.
Harry Potter is a very powerful wizard. The generation he was born into is very powerful and he is the most powerful of them all. The reason for this is simple and tragic. Magic can neither be created nor destroyed. There exists on the planet earth a finite amount of magic, equally distributed across its surface. Every magical life that dies releases its magic only to be absorbed into the next magical life born. There is a balance between the magic that exists in the non-sentient and the magic that exists in the sentient. At the time of Harry's birth due to the evil of Voldemort and his willingness to kill entire families including the children there was an imbalance in the nature of magic. To correct the balance all the unattached magic was redistributed amongst the surviving children in proportion to how powerful they were supposed to be. That by itself made Harry Potter a very strong wizard. So strong that as a baby his parents allowed his magic to be bound to protect him from himself, a practice that had come into favor toward the end of the war with Voldemort as so many children to the glee of their parents were showing amazing early power. Most didn't think the binding worked as their children continued to show impressive bouts of accidental magic. Harry Potter became even more powerful when his parents and Voldemort became the last casualties of the war. His parents magic affected by the strong bond of love and duty being expressed at their deaths combined with nature's saturation of magic bonded with Harry. Most of Voldomorts magic was protected by his hocrux's except for the magic contained in the small piece of his soul he split with the intention of creating his final hocrux to insure his immortality. That piece imbedded itself in Harry's forehead along with the magical cores of his parents leaving behind a scar.
Most people know the series of events that followed that left him in the abusive care of his aunt and uncle. What most people don't know is what was happening in his scar. In harrys scar lived three ghosts. Harry's parents driven by their love and duty and a piece of Voldemorts corrupted soul. To Harry's parents the soul fragment just seemed like a petulant child that was in need of parenting and so they accepted the challenged and built a spiritual home in the scar on Harry's head.
Three year old Harry Potter was in the kitchen trying to make breakfast for his aunt and uncle. This was the first time his aunt Petunia "allowed" him to do it on his own and he was determined to get it right. The las thing he wanted to do was earn his uncle's wrath for messing up his favorite meal. His uncle especially scared him as he had started to become more and more physical with him and he had sinking feeling that while he had never been beaten, it was just a matter of time. His uncle seemed to become enraged at the Harry for any and everything and the taunts were becoming more vicious. Harry shudder at the remembrance of the look in his uncle's eyes when he had told Harry that his mother was a whore. When Harry confusingly asked what a whore was, he was sure he was about to get pounded but his uncle had been distracted by some children who had thrown a ball into their yard at 4 Privet Dr.
Unfortunately his distracted thinking caused him to burn the bacon. He quickly went to bin it so he could start some more when his uncle walked into the kitchen. Later Harry could not fully remember all that had happened. He remembered his uncles yelling about wasting food and he remembered being grabbed and thrown into the living room and told to go back to his cupboard under the stairs. He doesn't know why he didn't remember making it in time but he remembered the pain of the fireplace poker snapping his arm. Then he remembered the pain stopped and a bright flash and then darkness.
When Harry Potter woke up, the first thing he noticed was that it was very quiet. Usually he enjoyed when it was quiet because it meant he wasn't being yelled at but this was a different type of quiet. There was absolutely no sound. The central air that was constantly running was silent as was the fridge and all the appliances. Harry couldn't hear any sounds of animals or people outside or cars running. For the three seconds of silence, Harry thought he had gone deaf but then he heard his uncle groan. As fear started to build up inside him he heard a soft beautiful voice call his name. He looked up into semi-transparent green eyes and something clicked. "mum."