The corners of a typical rectangular kitchen sink are quarter-circles. The larger the radius of the circle, the more "round" the corner appears. When the corner is a 90-degree angle, there is no circle and therefore no radius, hence the name "zero-radius." A true zero-radius sink has all 90-degree angles, so it looks like a box.
Zero-radius sinks are usually made of stainless steel. They are almost always under-mounted--attached to the bottom of the countertop rather than dropped in with a rim that rests on top of the counter, which is how most kitchen sinks are mounted.
Zero-radius sinks give a kitchen a professional look. They offer plenty of room for food preparation and cleanup. Flat-bottomed models allow you to stack a lot of dishes with less risk of them tipping.
Sharp zero-radius corners are harder to clean than rounded corners, which you can easily swipe with a sponge. Flat-bottomed models might not drain very well.