Сей (feminine сия, neuter сие) is an archaic pronoun similar to "this" in English. Some time ago, it was for indicating the closest object as the opposite to тот (that). It became obsolete, but is still a part of some very ordinary words:
Сегодня = сего + дня, literally, by this day.
Сейчас = сей + час, literally, this hour.
Sometimes native speakers use this word to give their speech a "high style" flavour, to make is more elegant. Sometimes it works, but more often that that it doesn't.
За сим разрешите откланяться - a common 19th century phrase to finish the letter. "And after [saying] this, let me bow to you".
Посему я решил... - Again, "посему" is a common word for 19th century. " Because of that"...