"Please switch off the air conditioner."
If you put your mouse over the word 了, you see that it is an interjection in this case. Wikipedia says that "in linguistics, an interjection is a word or expression that occurs as an utterance on its own and expresses a spontaneous feeling or reaction"
Meanwhile, it is weird to say it without the 了 because the sentence would feel incomplete. Instead of using 关了, you use 关 and a preposition e.g. 关掉 or 关上 to have a complete verb
I think in this case, 了 is expressing the "new situation" of the air conditioner being off (that will be a new situation, because the air conditioner is on now.) However, you need to put something where the 了 is in this sentence. When you use the 把 sentence structure, you can't end it with a single character verb. There has to be some kind of complement after the verb. So 了 is filling a grammatical need here.