The visualizing itself doesn't strengthen the memory. What strengthens the memory is that it is related to another long-term memory so that it also becomes a long-term memory. The weaker memory becomes part of the stronger memory so that it also becomes stronger in the process.
For example, you wanted to remember the name of somebody named Thomas Rex, you might relate him to a long-memory of a certain type of dinosaur. If you wanted to remember that rex in latin means king, you might refer to that same type of dinosaur as being king of the dinosaurs.
Visualization is used because the long-term memory you are connecting your desired memory to is one that occurs over time, so you have to visualize it to recall the entire memory. Remember, the long- term memory you should be using is the point of the recalled dream where you noticed a dream sign. After you visualize that, you continue the visualization, only with you realizing you are dreaming. After that you state your intention, something along the lines of "Next time I (experience) (the dream sign missed) I will realize I'm dreaming. You are basically trying to learn from the mistake with the intention of not making the same mistake next time.
All of this I'm preaching here comes from the original MILD technique by Stephen Laberge, which I think is the best one. His book
Exploring the World of Lucid Dreaming is handily available for free on pdf here:
http://www.bibliotecapleyades.net/ar...iddreaming.pdf. His MILD technique is spelled out on page 58. He emphasizes on prospective memory a lot, but how the memory is strengthened is what makes the prospective memory possible.