Think of a braided rope and that will give you an idea of what a braided trail is. Instead of a single width trail hikers will often try to avoid the wet and muddy sections to keep their feet dry causing the trail to become wider and wider. In very bad areas there will be multiple areas on both sides of the track that can turn into a muddy bog. This behaviour often creates damage to environments that are very fragile and take load period to repair.
The recommendation is to stay on the designated trail which will mean walking through the wet areas.
An example of a braided trail. The main trail is on the right hand side of the image with the mud clearly visible. In an attempt to avoid this muddy area hikers have created a new trail on the left.
Braided trail on the Tasmanian South Coast Track as hikers try to avoid getting their feet wet
This boardwalk on the Overland Track stops an area like this turning into a mud pile