He was talking about dying spirtually because you see that as soon as they ate the fruit they knew good and evil. Spiritually, they were not alive and Holy. As God said in Genisis 3:22 "And the LORD God said, Behold, the man is become as one of us, to know good and evil:.." Here, i think he was referring to Himself, the angels, and satan and his demons because they know all these things. But was is interesting is the second part of this verse: "...and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:" Later in verse 24 it explains that this is why he put the flaming sword at the gates of Eden so No one can get to the tree of life: "So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life."
I don't know why this tree was not mentioned in the beginning but God did not want any man to eat from this tree either.