With a two year old and a three year old you have to find the right balance when discussing extreme weather. You want them to take it seriously, but to not be terrified.
Ironically, my kids know what a "twister" is because of an episode of Wonder Pets. They enjoy singing the line, "They go round, round, round picking stuff off the ground." They know that sometimes there is a tornado warning which means that there might be a tornado nearby.
Last night a series of storms pushed through our area and we decided we needed to upgrade our plan of going to the basement with the kids and huddling in the darkness at the bottom of the stairs. We cleaned out the basement closet and put blankets, pillows, flashlights, snacks, water bottles, and a couple of just-in-case diapers in there. We also loaded up the iPad with episodes of Handy Manny.
Of course, by the time we got all that done, the storms had pretty much passed through, but by then the kids were excited about the "hidey cave" and so we went down there anyway and watched an episode of Handy Manny just to test it out. The kids loved it and protested when it was time to leave.
All in all, it was a pretty good upgrade of our What to Do When There's a Tornado Warning Plan and a great dry run. Now we just have to figure out what to do with all the stuff we pulled out of that closet and tossed into the center of the basement.