The Simplify command reduces the number of coordinates that define an object. Given a scope of action ([All Objects] or a selection) and a Distance, the Simplify command will reduce the number of coordinates such that the coordinates that define the object are approximately the given distance apart. The Remove small branches option will automatically remove branches in multi-branched objects (such as areas with islands or holes) that are smaller than the given distance.
In the example above, the province of Durango in Mexico has been simplified using Simplify. The drawing was first projected into Orthographic projection so that meter-based distances could be used.
The Simplify dialog was run with a Distance of 25000 meters.
Comparison to Normalize Topology
The Simplify command is similar to the Normalize Topology transform toolbar operator. However, the Simplify command is aimed at simplification on a per-object basis while the Normalize Topology operator considers relationships between objects when simplifying them. We can see the difference by running both commands on a drawing of Mexico.
We begin with a drawing of Mexico that's been projected into Orthographic projection.
Running Simplify with a distance setting of 25000 meters results in the simplification of areas. However, each area is simplified without considering any relationships with adjacent areas. This provides an optimal simplification when each area is considered by itself but also results in overlaps and gaps between areas.
If instead of using Simplify we used Normalize Topology, we would first use View - Properties - Precision to set the Location Precision to 25000 meters and then we would run Normalize Topology.
Normalize Topology takes a lot longer to run than Simplify, but the result in the end is free of overlaps and gaps. Each area has been adjusted both on the basis of capturing its own shape as well as to match its neighbors. However, it could be said that the resulting shape for each individual object (without regard to neighboring areas) is not as "optimal" a simplification as is done by Simplify.
When simplifying a single object it is probably best to use Simplify since the result is obtained much faster. When simplifying many objects for which adjacency must be maintained it is best to use Normalize Topology.