1Refers to the period from now onward — a somewhat formal way of saying 'from now on' or 'from this point forward', often in the pattern 以後、〜.
以後、遅刻しないように気をつけます。
From now on, I'll be careful not to be late.
この規則は来月以後、適用されます。
This rule will apply from next month onward.
以後お見知りおきを。
Please remember me favorably from now on.
以後、この件について一切回答いたしません。
From now on, I will not respond to this matter at all.
2Indicates the period following a specific event or point in time — used as あれ以後, それ以後, or after the -te form of a verb, close in meaning to 'since then'.
あの事件以後、彼は外出を控えている。
Since that incident, he has been avoiding going out.
卒業以後、彼とは一度も会っていない。
I haven't seen him even once since graduation.
開店以後、売り上げは伸び続けている。
Sales have kept growing ever since the store opened.