The ritual of kaparot [lit. atonement], which is usually done just prior to Yom Kippur (usually the day before), where one waves a chicken or an [unspecified] amount of money over one's head in a circular motion three times while chanting a text, and then gives the ritually used object to charity, seems difficult to understand. If charity can atone for sin, why does one need to wave it around one's head? Can this ritual be performed any time of year? Where did the idea of chickens come from, and why a chicken more so than any other animal?
Kitzur Shulchan Aruch (131:1) states:
ואל יחשוב האדם שזוהי כפרתו ממש, אלא יחשב כי כל מה שעושין בעוף הזה, היה ראוי לבוא עליו בעונותיו. ויתאונן על חטאיו, והקדוש-ברוך-הוא ברחמיו יקבל תשובתו.
A person should not think, however, that this ceremony itself actually atones for him. On the contrary, [he should look at the ceremony as symbolic in nature, realizing] that everything that is being done to the chicken should really be done to him [as punishment] for his sins. [This will make] him regret his sins, and, as a result, the Holy One, blessed be He, in His mercy, will accept his repentance (3). (Translation from here)
Nitei Gavriel Yom Kippur 10:2:4 says that a chicken was selected for the following reasons.
A: It is not too expensive.
B: It should not seem like a Korbon (Makriv Kodoshim BaChutz). And a chicken is not used as a Korbon.
Nitei Gavriel Yom Kippur 10:17 says that it can be done also with live fish and money, and you also wave the money around your head.
Nitei Gavriel Yom Kippur 10:7 says that if it was not done during the Aseres Yemei Teshuva it may be done on Hoshana Raba. It seems from here that it is specific for this time of the year.
See The tur in 605
He also says
That even though a domestic animal (not a bird) is more expensive than a rooster is preferred becouse it is called "gever" (also meaning man (see yuma 20b))...
See the maharal m'prag's book
נתיבות עולם - נתיב הבטחון - פרק א
To summarize one of the ways to understand this paragraph (if I am wrong please inform me in a comment)
it is known that the source from the gemoro to take a chicken for a kaporo of your soul on erev yom kippur, is
Talmud brochois 60b bottom
the following incident. R. Akiba was once going along the road and he came to a certain town and looked for lodgings but was everywhere refused. He said 'Whatever the All-Merciful does is for good', and he went and spent the night in the open field. He had with him a cock, an ass and a lamp. A gust of wind came and blew out the lamp, a weasel came and ate the cock, a lion came and ate the ass. He said: 'Whatever the All-Merciful does is for good'. The same night some brigands came and carried off the inhabitants of the town. He said to them: Did I not say to you, 'Whatever the All-Merciful does is all for good?
He also writes that as he says before (in the same book) these 3 things (ass, rooster and candle) are the 3 parts of a person body, soul and mind
The body is course and is fit for a donkey (for the soul to ride on)
The soul is fit for a rooster that is called gever and ish
(It is know that The soul is the form and is called ish and a ass is called isha...)
And the lamp is across the mind, the mind shines for a person and every place the mind is called lamp (in shabos 23b it says that the one that is careful with lamp (shabos candles) will have children that are talmiday hachomim)
Since Rabbi Akiva came to this city he also was suppose to get what the city got, meaning to get captured and if he would be captured his body, soul and mind would aslo be captured (since they will keep him busy)
Hashem wanted to save Rabbi Akiva, since he was in the city the decree (to be captured) that was on the city also was on him, so it can't be that the decree will not effect him, it can't be that it will not have any affect on him
so Hashem made him loose his ass, rooster and light instead (this was his exchange)
(becouse of his belief in Hashem what every thing he does is for the good Hashem did for him somthing that looked bad but was good)
So it seems Acording to the maaral mprag
that it is a kaporo of your neshomo every time your rooster dyes, anytime of the year but before yom Kippur we want to atone (exchange for) our souls for (before) yom kippur
And it is not required to wave it around your head, it is just symbolic
The minhag was that the same chicken afterwords was used for the mitzvah of the meal before yom kippur (some people still do it today)
https://www.youtube.com/watch?v=YKVlMMbTI9s [WARNING: Video contains actual depiction of idolatrous rituals]
It does not "work" and it should absolutely not be performed. It is a clear act of darkhei emori according to Rav Hai Gaon, the RambaM, the RambaN, the Beth Yosef, and others.
And if you can watch the link above and tell me that "the Satanists copied the ritual from the Jews" then all honesty with ourselves may just be lost, has wa-shalom.
Note: The "kapparot" ritual begins around 11:20 of the video.