The term 'make headway' can be defined as making progress or achieving success. The crossword solutions for this term are 'ADVANCE' (7 letters), 'GAIN' (4 letters), 'PROCEED' (7 letters), and 'CONTINUE' (8 letters). All of these words imply forward movement, suggesting that the person is making progress in some way. This could refer to any kind of progress, such as making progress in a project, advancing in a career, or gaining ground in a competition.