Got any links? Never heard of Tesselators, and google didn't help much either.
I'm not sure what it is, exactly, but I know what it does.
It draws quads (4-sided polygons in 3D space).
Example:
tessellator.addVertexWithUV(minX, theY, maxZ, minU, maxV);
tessellator.addVertexWithUV(minX, theY, minZ, minU, minV);
tessellator.addVertexWithUV(maxX, theY, minZ, maxU, minV);
tessellator.addVertexWithUV(maxX, theY, maxZ, maxU, maxV);
Draws a single plane on the X/Z plane (i.e. the top of a block). Flipping the points around (reverse order) will render it upside down (i.e. bottom of a block). Not sure what the orientation is of those four lines offhand, though. I think it's the underside, based off a comment in the code referencing the "bottom of the bed" where I got it from.