To make progress or advance toward a goal; to move forward despite obstacles or difficulties.
This nautical term originally described a ship's forward progress through water, particularly against wind or current. 'Headway' in sailing refers to the forward motion of a vessel, and the phrase moved into general usage in the 18th century to describe any kind of progress or advancement.
The nautical origin is particularly apt because making headway at sea often requires skill and persistence against natural forces - wind, current, and waves. This background gives the phrase an inherent sense of earned progress through effort, rather than easy advancement.
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