There are words where we say A as Ai, and say A as Ah. First I thought there were some sentences where it sounds better then the other. However, when Koreans say Amen they say it as "Ah-men", and I keep hearing Americans say it as "Ai-men". What is the reason for this?
In most dialects of English, 'a' is normally pronounced either /æ/ or /ɛɪ/, as in "man" and "mane". There are relatively few words where it is pronounced /a/ (as in "ah"), and they tend to vary quite a lot with dialect (eg "pass" and "graph" have that vowel in SE England, but not in most of the English speaking world.)
Normal English spelling rules would make "amen" either /ə'mɛn/ (like "amend"), or else /'ɛɪmən/ or /'ɛɪmɪn/, (a bit like "aiming" , but with "n" at the end rather than "ng").
Presumably because of either its foreign origins or its ceremonial character, this is changed into an unusual pattern for English, with full (unreduced) vowels and with either final stress (US /ɛɪ'mɛn/) or even stress (British /a:mɛn/). Even with the unusual stress pattern, the US version has a more regular vowel /ɛɪ/ and the British a more exotic (and slightly truer to its origins) /a:/. I don't know any particular reason why the two varieties of English should have settled down to different realisations of this word.
Since the English /ɛɪ/ is a result of the great vowel shift, few other languages have a remotely similar vowel for "a"; so one would expect to find /a:/ for the word in places which either have not been influenced particularly by English, or have taken it from British English; and /ɛɪ/ only in places where the word has been adopted from American English.
It's all due to the nationalities and the pronunciation that is more commonly used in different countries. For example, in South-East Asia, "Amen" is also pronounced "Ah-men". This is because of the fact that "a" in South-East Asia, is (nearly) always pronounced as "Ah". However, Americans tend to pronounce "a" as "ai." British also tend to pronounced "a" as "ah" (depending on the region the speaker came from), but Australians generally say "ai-mmen".
Basically, it's all due to how "a" is usually pronounced in the region, or country, or native-language(especially when English is not the first language of the speaker).