Although circumcsion most likely originated and arose independently more than once, such as evidenced amongst the Aboriginal peoples and related populations in the South Pacific, our current and dominant tradition of circumcision is a relict tradition of the original proto-Afroasiatic/Afrasan peoples, who lived around 17-11 YBP, and lived in present day Northeast Africa, inhabiting a stretch of southern Ethiopia north into northern Sudan and Eritrea.
It seems that the dominant tradition of male circumcision (which I assume is being referred to) and (possibly) female circumcision (termed FGM) both arose as a religious/spirtual surgical tradition amongst the early Afroasiatic/Afrasan peoples. Aside from the religious beliefs associated with circumcision, it also had social/cultural importance as well due to virginity, especially female virginity, having a very high level of importance in proto-Afroasiatic/Afrasan society. Hence, female circumcision was (and still is) used as a way to reduce the chances or a female/young woman engaging in loose behavior and as a means to preserve her chastity.
An important religious association of circumcision was also how circumsized persons were spirtually 'pure' and could engage in the religious pagan proto-Afroasiatic/Afrasan and early and later derivative pagan and Abrahamic religious traditions. Circumcision was probably also used to differentiate between 'us' and 'them', and served to further strengthen in-group social identity and cohesiveness, as evidenced by later Afroasiatic/Afrasan peoples disdaim for the 'uncircumcised'.
Prior to the the worldwide spread of Islam, Christianity, and Judaism, and earlier Afroasiatic/Afrasan religious and social traditions, circumcision was (mostly) restricted to the Afroasiatic peoples, such as the ancestral Cushitic (Somali, Iraqw, Beja), Berber (Tuareg, Riffians, Kablye), Semitic (Arabs, Assyrians, Jews), and Egyptian, as well as Chadic (Hausa, etc.,) peoples, and first spread via cultural influence during the proto-Afroasiatic/Afrasan era to the neighboring early/proto-Sudanic (Ancestral Nilo-Saharan) peoples who lived to the east of the proto-Afroasiatic/Afrasan peoples, and later on, their descendant proto-Cushitic people.
I also believe that it was through contact with Cushitic speakers that the Bantu and ancestral Bantu peoples also adopted circumcision early on (3-2000 BCE), as such interaction is supported by heavy-to-nominal Cushitic genetic admixture in Bantu populations from CAR and Kenya, into the Great Lakes region, and well into South Africa and Congo, and the adoption of cattle and other animal domesticates and semi-pastoralism/pastoralism by Bantu groups, alongside the linguistic influences that various extinct Cushitic tongues and languages had/have on Bantu languages.
For West Africa, it was either transmitted via the Cushitic-influenced Bantu peoples to their West African Niger-Kordafian non-Bantu and Bantu counterparts, and/or by the Sudanic and Afroasiatic Chadic migrants from the Sudan who migrated westwards into Nigeria, Ghana, and further into Senegal and the Gambia, and south into the Cameroons. The Chadic/Sudanic is more likey, as is evidenced by the prevalence of FGM (female circumcision) in West African countries and regions with Chadic and Chadic-related historically pastoral groups such as the Hausa and Fulani, and regions with large numbers of 'Pulaar' (Fulani) speakers.
Since Judaism, Christianity, and Islam are responsible for the vast spread and adoption of circumcision outside Africa and in Europe, South/Central Asia, and the Americas, we can explain as why Judaism, Christianity, and Islam all had role to play in the widespread adoption of circumcision by posing this question, why is circumcision an important part of all of these faiths?
Islam, Christianity, and Judiasm are the three religions that make up the Abrahamic religious tradition. All three religions had their roots in the Semitic peoples, with Christianity and Judaism first arising amongst the Jews and Islam amongst the related Arabs. The Semitic peoples, such as the Jews and Arabs, are an Afroasiatic/Afrasan peoples, with their cultural, religious, linguistic, and (alot/most/all) of their genetic ancestry tracing back to the ancestral Semitic peoples and proto-Semites. The proto-Semites first arose and were the product of Afroasiatic/Afrasan migrants from Egypt into the Levant (Syria/Lebanon/Israel), and an indigenous non-Afroasiatic/Afrasan Levantine people and culture who seemed to have been fully assimilated by the Afroasiatic/Afrasan migrants who carried with them the earlier mentioned Afroasiatic/Afrasan traditions of circumcision with all the religious/spirtual and social baggage that came along with it. The arising mixed population, called the Natufians, are seen seen as having preserved alot (if not most?) of the Afroasiatic/Afrasan religious traditions, such as evidence of having preserved the traditional proto-Afroasiatic/Afrasan clan-priest of their Afroasiatic/Afrasan forebears, and circumcision.
With the expansion of the Semitic speakers from their ancestral homeland in the Levant and into the Arabian peninsula and Mesopotamia, they divide, with several Semitic dialects and peoples, such as the Assyrians, Northern Semites (ancestral to Jews, Canaanites), Central and South Semites (ancestral to Arabs and South Arabian peoples) coming into existence and later dividing up even further. The Afroasiatic/Afrasan religious and social traditions, including circumcision, was most likely present amongst all these Semitic groups. Hence, the Hebrew and Arab peoples, having inherited and preserved the religious and spirtual Afroasiatic/Afrasan traditions of their Natufian forebears, such as circumcision, maintained these ancestral traditions with their religious and social associations, which they later incorporated (or better said, maintained) in the religious traditions (Judaism, Christianity, Islam) which then arose amongst these groups, wherein they later spread with the dispersal of the Jewish people, the later Christian and Islamic conversions and expansions into pagan Europe, Asia, and Africa, and later on, with European colonization of the Americas, etc.,.
However, I would like to reiterate how circumcision was not solely practiced by and only arose amongst the early Afroasiatic/Afrasan peoples, since the Aboriginal and other related South Pacific (Polynesian? Melanasian?) peoples also have practiced (and still do) circumcision prior to any tangible contact and exposure to any Afroasiatic/Afrasan peoples and traditions. I've also heard of circumcision also having possibly arised independently amongst the Uto-Aztecan and/or other Mesoamerican and American groups, with both the American and South Pacific/Australian traditions of circumcision having somewhat vaguely similar religious/spirtual associations as well.