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 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.
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.
Were there many cars on the road? I've got so many things to do this morning. You've given me too many potatoes (= more than I want). There aren't as many people here as last year.
A large number of persons or things: "For many are called, but few are chosen" (Matthew 22:14).