What does it mean that Men become divine (gods)?

Another way of considering this is to ask in what way resurrected Men in Heaven differ from mortal Men on earth. 

The key explanatory concept is that God is the creator - the prime creator: creator of Men and of all creation.

(...But not creator of every-thing - there was/is already primordial chaos. Creation is from chaos, by God.) 

The difference is that in Heaven we work with God, inside God's creation - among only those Men who do likewise. In Heaven there are only those men who have (like ourselves) made a permanent commitment to God's loving plan of creation. 

(So there is no evil in Heaven - because evil is the purposive destruction of creation.)

Heaven is bound-together by love, and directed-towards creation: creation is, at a deep level, the intrinsic consequence of love. 

In Heaven, whatever creation we do (according to our disposition) beomes a part of God's already-existant and on-going creation; harmonised with it by loving affection and being directed to the same goals. 

(And Heavenly creation includes pro-creation - the begetting of spirit children, who may in turn then choose to incarnate, die, and follow Jesus Christ to Heaven.) 

So, to be divine is to participate-in divine creation. To some extent, and temporarily, this may happen on earth during mortal life. But full divinity is self-conscious, chosen, eternal participation.