Many is used only with the plural of countable nouns (except in the combination many a). Its counterpart used with uncountable nouns is much. Many and much merge in the comparative and superlative forms, which are more and most for both determiners.
You use many to indicate that you are talking about a large number of people or things. I don't think many people would argue with that. Not many films are made in Finland. Do you keep many books and papers and memorabilia?
Many, innumerable, manifold, numerous imply the presence or succession of a large number of units. Many is a popular and common word for this idea: many times. Numerous, a more formal word, refers to a great number or to very many units: letters too numerous to mention.
“Much” is used with uncountable nouns, such as “water” or “time,” while “many” is used with countable nouns, like “books” or “apples.” Both words can appear in negative sentences, questions, and formal expressions, but in positive sentences, they are often replaced by “a lot of”.