This page was created from Joel's Interactive Guide to Straight Razor Shaving and can be discussed in this thread.
The grind of a razor is essentially how the blade is designed, or rather, the particular characteristics. A "wedge" razor is going to be just that, a wedge. Wedge razors are both the heaviest, and the most robust razors, and are often the best for gentlemen with a very tough beard. Typically, the heavier the grind, the easier it will plow through tough beard growth, however due to the incredible stiffness of the blade, it will not contour to ones face at all, and these blades often do not provide as close of a shave as can be had with an extra hollow ground "singing" razor. If viewed head on, it appears to be a "triangle".
The opposite, or rather "antonym" of the wedge is the full (or "extra") hollow ground razor. Full hollow ground razors are also known as "singing" razors, as the sides of the blade are ground to such an incredibly thin sliver of steel the razor makes a singing note as it is stropped, or when the front of the razor (in between the head and the point) is plucked with ones fingernail. Hollow ground, or now often called "Extra hollow ground" straight razors are by far the most difficult razor to make, and as a result are often the most expensive. It takes many years of experience for razor makers to fine tune their skills/abilities to successfully make extra hollow ground razors, and even the most skilled straight razor makers often have to throw out a good percentage of blades they make, due to mistakes, breakage, etc. "Singing" razors are considered by most to be the closest shaving razors, as they're incredibly sharp, and incredibly delicate edges can actually bend/flex to the contours of ones face, thus allowing you to get THE closest shave possible.
As you can see, the full hollow ground razor has a MUCH different profile than a wedge.
There are also razors in-between these two categories, such as ¼ hollow, ½ hollow, concave, etc. Concave razors are exceptionally uncommon and are no longer manufactured to my knowledge (unless it is a custom one-off razor) so let's not waste time on those. Basically, the less metal ground out or "hollowed" the stiffer the blade will be in the case of straight razors. The less hollowed the blade, the stiffer the blade.
Typically for heavy bearded gentlemen, wedges, ½ hollow and ¼ hollow blades work best, but this doesn't mean a gentleman with a light beard cannot, or will not get an exceptional shave with a wedge--or visa versa--as a very heavy bearded fella can get a superlative shave from a singing razor as well. Grinds are more personal preference than necessity, but the basic rule of thumb is the heavier the grind, the easier to shave heavier beards; and the thinner the grind, the finer the edge, the closer the shave, and easier to hone as there is much less metal to remove.