It was one of those dreams which

You know what a dream is, right?

while retaining the characteristic dream scenery

Very often the things you "see" in a dream are somehow not realistic (and this often makes you aware that it's a dream).

are a continuation of one’s intellectual life

While there may be "scenery" differences from "real life", much of the structure of this dream is realistic and relates to thoughts and concerns you have when awake.

and in which one becomes aware of facts and ideas which still seem new and valuable after one is awake

Some of what you remember from the dream seems to provide new insights into your "awake" life.

It was one of those dreams which

You know what a dream is, right?

while retaining the characteristic dream scenery

Very often the things you "see" in a dream are somehow not realistic (and this often makes you aware that it's a dream).

are a continuation of one’s intellectual life

While there may be "scenery" differences from "real life", much of the structure of this dream is realistic and relates to thoughts and concerns you have when awake.

and in which one becomes aware of facts and ideas which still seem new and valuable after one is awake

Some of what you remember from the dream seems to provide new insights into your "awake" life.

A classical example of this (though admittedly not particularly "realistic") is Friedrich August Kekulé's dream about snakes that led him to the structure of the benzene ring.