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?
Definition of many determiner in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
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.
many or much? Many is used with words for things that we can count. Much is used with words for things that we cannot count. Compare: Do you have many things to do today? Do you have much work to do today? I didn't eat many cookies. I didn't eat much cake.
A large number of persons or things: "For many are called, but few are chosen" (Matthew 22:14).