What a rounded edge buys you
A square, sharp edge on cured concrete is fragile. It has nothing supporting it on one side, and a dropped tool, a mower wheel, or the corner of a car tire clipping it chips that edge off cleanly, leaving a mark that never goes away. Rolling the edge into a small radius while the concrete is still soft removes that weak point. The rounded edge takes the same knock and shrugs it off instead of chipping.
It also reads better. A crisp, consistent edge around a driveway or a patio is one of the things that separates a slab that looks finished from one that looks poured and walked away from, and it is one of the first details anyone notices without being able to say why.
Where it happens on the slab
Edging happens at two places on most pours: the outer perimeter where the concrete meets the form boards, and the sides of any joint that gets tooled in rather than saw cut later. Both use the same motion, running the tool along the line while the concrete is firm enough to hold the shape but soft enough that the tool does not tear it.
The crew edges early in the finishing sequence, right after bull floating and before the surface texture goes on, then usually comes back for a second, lighter pass once the concrete has stiffened a little more, to clean up any marks the first pass left. Forms come off after the concrete has cured enough to hold its shape, and a well edged perimeter is the reason that edge stays clean once the wood is gone.
What a skipped or rushed edge looks like later
Skip edging, or rush it before the concrete is ready, and the perimeter is the first place a slab shows its age. Sharp, unrounded corners chip within the first season of normal use. A pass that is too heavy, or done too early, can also pull the coarser aggregate right to the edge and leave a rough, exposed strip that looks and feels different from the rest of the slab. Neither is a structural problem, but both are the kind of detail that is cheap to get right during the pour and expensive to fix afterward.
Once the concrete has cured and the forms come off, there is no going back to reshape that edge. Any repair at that point means grinding it down or patching it, and a patch on an edge rarely blends the way the original pour does. That one pass with the edging tool, done at the right moment, is the only chance the perimeter gets.