"I made an appointment for tomorrow" means that the appointment will occur tomorrow.
"I made an appointment tomorrow" makes no sense, because it is trying to say that the time at which the appointment was made is tomorrow. This is impossible, because tomorrow is in the future, but the word "made" is in the past tense.
I agree with ToB. "I made an appointment tomorrow" makes no sense; "for" is required. "For" in this case indicates that the appointment will occur tomorrow. It does not mean the same as the "for" in "What are we going to have for dinner?" "For" has lots of meanings.
"For" here means "which will take place", bamboo.
However, native speakers do not say "I made an appointment which will take place tomorrow". "I made an appointment for tomorrow" is a natural and common way of expressing the idea.
Very often, "for" cannot be replaced by a single word.
But if I use a day of the week (e.g. Friday) in place of tomorrow, should I use "for" or "on" or are both correct?
"I'd like to make an appointment on Friday please?"
"I'd like to make an appointment for Friday please?"