Rashi mentions a custom mentioned by the Geonim that “twenty two or fifteen days” before Rosh Hashono people would take baskets – one for each child – and plant legumes and the like, and before Rosh Hashono would wave them around their heads and say, “This should be instead of this [person], and it should be my exchange, and it should be my substitute.” The baskets would then be thrown into the river. In this Rashi we find the concept of saving oneself from a harsh Heavenly decree by it being effected on another object.
The Maharal writes that the Gemoro implies the same. The Gemoro brings the story of Rabbi Akiva who was travelling with a donkey, and rooster and a candle. Upon being refused entry to a certain city, Rabbi Akiva had no choice but to sleep overnight in the woods outside the city. During the night a lion killed the donkey, a cat devoured the rooster, and a wind extinguished the candle. The next morning he learned that the city had been attacked by murderous thieves and he had been miraculously saved. The Maharal explains that the same terrible fate that the townspeople had suffered, was to befall Rabbi Akiva as well. However, he was substituted by his donkey (representing his physical body), his rooster (instead of his soul) and the candle (instead of his intellect). The Maharal concludes that from this Gemoro we have an “absolute proof to take a chicken for a kaporo for the soul on erev Yom Kippur.”
The Remo brings this custom in Shulchon Oruch and writes that it is a custom of pious people and should not be disregarded.
In addition to the afore-mentioned dimension of kaporos being a “substitute” for the individual (as the Mishna Berura writes that the individual should imagine that all that is transpiring to the chicken should in fact have happened to him), there is another reason which is brought down in Eliya Rabo, that the kaporos is an atonement for the sins of the person. This being the case, it is likened to an obligatory sacrifice that each individual has to bring. (The halachic implications of these opinions will later be discussed.)
However the Kitzur Shulchon Oruch writes that the individual should not think that the chicken is literally his atonement. It should merely serve as a reminder that all of these things should have happened to him, thus arousing him to repent fully.
It is obvious from the authorities that the main part of the custom of kaporos is the slaughtering of the chicken. Especially considering the abovementioned objective of kaporos, that the individual realise that everything happening to the chicken should have happened to him.
Furthermore one of the criterion mentioned with regards to kaporos is that it should be conducted in the early morning. Both these points are evident in the words of the authorities.
In Shulchan Aruch the mechaber writes that this which they are accustomed to do kaporos on the eve of Yom Kippur to slaughter a chicken etc. Similarly in the Mogen Avrohom in the name of the AriZal and the Shalo.