If you haven't had the pleasure (or maybe the distaste, for some people) of taking Mad-Eye Moody's Defense Against the Dark Arts class, do not fret. Not only was the class actually taught by Barty Crouch Jr. disguised as Mad-Eye with the aid of Polyjuice Potion, but this particular clip from the Goblet of Fire will explain all you need to know about the three Unforgivable Curses:
Sends a shiver down your spine, doesn't it? It is unbelievable that spells exist that can truly damage, hurt, or even kill another witch or wizard, spells that can actually put you behind bars at the dreaded Azkaban with a life sentence. And we all know how being around Dementors in Azkaban is beyond torture.
According to akyser on Reddit, the 'Cruciatus Curse,' the 'Imperius Curse,' and the 'Killing Curse' were all deemed unforgivable, rather than just lightly punishable. But why these particular three?
askyser believes that these spells are the worst one could do to a magically inclined person, affecting their body, their soul, and their mind.
This curse will shut down the body and cause as extreme pain as one possibly can to the body.
The Imperius Curse will cause your mind to shut down, making you vulnerable to the caster and his/her will. This curse will make you do the bidding of the witch or wizard who performed the spell.
The Killing Curse
Spell: Avada Kedavra
This curse separates your soul from your body, causing it to pass into the magical afterlife. Once the soul is out of the body, the soul is frozen in time. This can be so damaging that it is the reason why a Horcrux can be created during the time of murder.
As Mad-Eye said, or rather Barty Jr., one must really mean it when you utter the spells that cast these unforgivable three. And for a wizard to have the ill-intent to destroy one of the three parts that make up a person, it means they are truly an evil, dark wizard indeed.