make headway
Synonym discussion
Sense: phrasal verb/1
'Make headway', 'progress', 'advance', and 'gain ground' all describe moving forward or improving. 'Make headway' specifically implies overcoming difficulty or resistance — you would use it when talking about slow but steady movement through obstacles. 'Progress' is the most general term (the project is progressing well) and can be used as both a verb and noun. 'Advance' often suggests organised, deliberate forward movement (troops advanced; technology has advanced). 'Gain ground' is the closest synonym but is less common and often used literally in military contexts or figuratively in competitive situations. For example: 'After the therapy, the patient made headway against the illness' emphasises the struggle, while 'the patient progressed well' simply states the improvement.
Etymology
'Make headway' comes from nautical language, where 'headway' referred to a ship's forward motion through water. By the 19th century, the phrase had been adopted more broadly to describe any kind of forward progress, especially when pushing against resistance — much like a ship battling wind and waves.