Phrasing and dynamics: these are what distinguish a musical tune from a mechanical string of notes. It is quite a rarity to see any phrase marks included in written-down scores of trad music, while it is the norm in classical music: but this doesn't mean you shouldn't try to phrase your tune. If you are an ear player, you will hopefully be able to feel where a musical phrase naturally ends, and the next one begins: a bit like taking a breath while singing. And never be afraid of brief silent gaps between notes: used appropriately, these will undoubtedly enhance your playing and also help you to keep the right timing: shortening long notes often leads to speeding up.
By dynamics, I mean louds and softs and all shades in between: for accordionists this means learning to use, or restrict use of, your bellows. Sometimes you can give an extra push or pull in the middle of a long note, which will add a new dimension to the tune.