Because walking takes us (usually) forward, the act of walking can be simply interpreted as the idea of making some progress.
Since walking is done 'on foot' it also implies making progress while going on one's instinctive understanding. This would be a most important point when the dream scene offers the possibility of using a vehicle of some sort, or if one starts out walking then changes to riding in a car, or goes from a car to walking on foot.
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