"Many" is just an (indefinite and subjective) number and hence an adjective. Whereever you say "many" you could also say "fifteen" or "one" or any other (definite or indefinite) number (many, some, all, ...), but also another adjective, say, "green".
Many people are left-handed.
Fifteen people are left-handed.
Green people are left-handed.
"Many of ..." is just the same but specifying the (sub-)group you talk about.
Many people are left-handed.
This says something about all entities you mean by people. "Many" is an adjective here. It would be possible to even leave the "people" out if it is clear what the subject is:
Let us talk about people. Many are left-handed.
"Many" is an adjective made noun here.
"Many of ..." will restrict what you say to a (to be specified) subgroup. The specification either happens by explicit declaration or using a pronoun or demonstrative:
Many of the green people are left handed.
Many of the people i talked about are left handed.
Many of them are able to write using their right handed.
The first and the second sentence attribute the left-handedness to a specific group, the third one references what was said before, perhaps the "left-handed [...] people i talked about" from above.
Demonstratives are back-references to something that has already been said, pointed at, etc.. This (you see? Here I reference what I have said in the sentence before.) is their function.
