Battledress is the clothes soldiers wear when they are actually fighting or working in the field, not the smart uniform they put on for a parade. In British English it often points to a particular khaki jacket-and-trousers set from the mid-twentieth century, though people also stretch it to mean combat clothes more generally. Dress here just means “clothes” — the same old sense you meet in evening dress or national dress — not a woman’s dress. It is a military, slightly old-fashioned word; ordinary speakers are more likely to say combat uniform or fatigues.