Tapering before a race allows your muscles to be "fresh" when the event comes. The point is to let your muscles rest, but still keep them active in the days leading up to a race. I don't think of it in terms of "easy" or "hard" but more "comfortable". You should not be pushing yourself right now, but doing what feels good for you.
Personally, I tend to run slower during my taper, but that is because I know that speed leads to shin problems for me. I do walk/run intervals, and take out my slower, older dog (I usually take my younger, faster one!) for my runs, just for a change of pace. This is what works for me, but it won't necessarily work for you. I've heard of a lot of people (particularly people who are fighting an injury right at the end) cycling or swimming in the week leading up to a race, instead of running. So basically take it easy, but don't stop moving!
Taper madness is something that gets you once you've cut down your mileage that you're used to making time for, and all that's left to do is pack and repack and check the weather reports every hour. It's mostly a feeling of excitement leading up to the race, but also a feeling of not having enough activity to put your energy into! I personally enjoy it a bit, even though I go batty. Don't even ask me how many times I've packed, already...

And I'm usually one of those people who waits for the day before to even pull out the suitcases!