It's ante meridiem and post meridiem. Let me explain. "dies" is the Latin word for day. It is in the e-declension. Not many words in Latin have the e-declensio

It's ante meridiem and post meridiem. Let me explain. "dies" is the Latin word for day. It is in the e-declension. Not many words in Latin have the e-declension. Another one is "res", the Latin word for thing. I don't know a lot about "meri", but it seems that "meridies" is also in the e-declension. "ante" and "post" are prepositions which ask for the accusative. The accusative is mostly lost in English, but often when you say "me", it's accusative. If you say "after I" it feels wrong. You say "after me". German has preserved the accusative, so it is natural for me. Now, in the e-declension the ending for the accusative is "-em". So you say ante meridiem and post meridiem.