...and you may be thinking what that has to do with gaming. Well, a memristor is a completely new component in electronics; no other combination of fundamental components can create it. It changes resistance based on the past flow of current: i.e., it is a resistor with memory. These two states can be interpreted as '1' or '0', and the states survive even when the power is turned off. In this way it can store data.

Since 1971, the memristor has been a theoretical concept; never proven in reality. A team from HP Labs has found ad described a real example of this behaviour discovered in a nanoscale system.

(Strukov, Dmitri B; Snider, Gregory S; Stewart, Duncan R & Williams, Stanley R (2008), "The missing memristor found", Nature 453: 80-83, doi:10.1038/nature06932)

A memristor has numerous possible applications. Two relevant ones are a transistor on a much smaller scale than currently available, and solid-state (non-moving; no noise) memory with access times as fast as RAM and not losing data when the power is removed. 

I'll say that again:

A solid state hard drive that can read and write data as fast as RAM.

How do you think that might be relevant to gaming...?

Wow. But we are years from gaming taking advantage of something like that

Wow this is really neat. We were just talking about resistors in physics class yesterday and the concept of a memeresitor sort of came up although no one called it that.

This could help PC's get insanely efficent if implemented correctly.
Harddrives are among the most major bottlenecks in modern computers along with certain types of wires/connections and eliminating these slowdowns would help massively up the performance!

Wow, the memresistor sounds so good. A solid state hard drive would an excellent alternative to current storage systems.

Do you know if it will take a long time to develop decent size hard drives? (E.g. over 50Gb)

Now there's just the question of cost...

 Exactly what I was thinking.

There are already applications using such a technology. I doubt the mainstream applications will ever get cost competitive with NAND and NOR flash. The current technology is under IP by one company, and since the actual benefits aren't leaps and bounds ahead of NAND and NOR flash, there will be no real benefit. I wouldn't expect a feasable way of using this around 2015, but by then there may be something else that is better.