"More " is used for comparisons; for example "I have more apples than you" or "the child has more brains than his mother". "Many" is an adjective used to modify nouns; "He has many friends". "She goes to many concerts". "Very" is a adverb and is used to modify adjectives, not nouns. "She is very intelligent".

More usually means más in Spanish. Many means mucho, but it is used to describe countable nouns, like many apples, bananas. And very means muy.