Literally: day – advance – month – walk
Alternately: Steady progress. A relatively smooth and rapid advance, especially of improvement or development in a positive direction.
Notes: This compound has a surprising construction. In general, 日X月Y means something is happening “day by day and month by month.” And 進歩 (shinpo) is “progress.” What’s unusual is that this compound is broken up for its parts to be slotted into the X and Y elements, where most compound-compounds just place two two-character blocks next to each other.
Some people apparently replace 進 with homophone 新, “new,” but this is an error.