Basically, the system has 1GB of main RAM for storing the data it's using, but some operations need to be accessed and worked on more quickly than others, so it has a 32MB bank of ultra-fast RAM for this purpose.

Basically, it makes certain techniques more efficient, or simply possible where they may not have been using just the slower main RAM.

Ahh okay, I understand now thank you.
But how does that help with anti-aliasing and anistrophic filtering? 

Seeing a discussion about Wii U hardware is like watching someone trying to lick their own elbow.

I already know that the CPU doesn't do nothing ... 

@Bold LOL, No! The reason screen tearing happens is exactly how I explained it. The reason it's out of sync is not because the GPU can't keep up like you thought but it's simply due to the fact that the display's refresh rate doesn't match with the video cards refresh rate. 

A v sync doesn't cause massive performance regressions and it's not intended to so it'll only drop by 3FPS at best. 

Well, anti-aliasing is one method that can be performed more effectively in eDRAM rather in the slower main RAM.

Another plus is deferred rendering; where multiple elements of a scene are rendered in separate frames then combined into one. This can be done better on Wii U (compared to PS3/360, anyway) because it's eDRAM is big enough to hold all the frames at once for fast, easy access.

You said yourself that v-sync is a double edged sword. The plus side it that it cuts out ugly and distracting screen tearing, which the 360 version of Bayonetta suffers from in abundance. The negative side is that it can impact framerate by locking the GPU down to a set rate instead of letting it tear frames to run faster.

The 360 version of Bayo opted to tear frames rather than make the framerate drop any further than it already does. Bayo 2 went the other way, enforcing a strict no tearing policy, likely because the GPU could keep a decent pace without going out of sync.

eDRAM almost doesn't do a damn to help anisotropic filtering cause textures need to be accessed through the main memory due to storage size constraints. Anti aliasing is a different story since ROPs are often far from utilized because of bandwidth limitations so blending on multisampled framebuffers in the eDRAM will provide some increase in performance due to the fact that the bandwidth bottleneck is somewhat relieved in the eDRAM. 

Geez, so many negative reactions. I read the article too, and I got the impression that it's a really beautiful game, just not 1080p/60fps, which I wasn't expecting it to be. I'm also glad to hear that Platinum is starting to get the hang of the Wii U. I like their games, so the better they get at developing for Wii U, the more comfortable they'll be when making games on it, and the more polished their games will look. Here's hoping they return to Wii U again sometime.

Locking a framerate is mostly optional ... V sync as the name implies only eliminates screen tearing. V sync will lock the frame time a display can refresh however it does not lock the average framerate. 

The negative like I specifically said was that it can manifest stuttering with variable framerates which is generally bad for controller response. 

Like I said before, v sync does almost nothing to your average framerate but it can potentially deliver frames inconsistently which will cause stutter.

Are we clear ? 

It's a topic about Wii U's graphics, they attract the detractors like catnip. ;)