Jude 2

When Jesus said He came to give us life and life more abundantly what exactly might that entail?

That He is not just about getting us to heaven, but he is with us to make our lives better here as well. We may not always understand everything He does in our lives, but EVERYTHING he does is to our benefit, even if we don't see it or understand it.

I read it and believe the Greek supports it to mean a much superior life in quantity and quality than before.

In context, I think His immediate meaning was that He came to set them free from the oppressive false faith of the Pharisees and a call to genuine life IN Him. But, I also believe that it can fairly be applied to the hope and reality of real life in Him without reference to false, oppressive faith.