How did they define a battle (two enemy armies fighting each other) if there was almost constant conflict at every single point on the front?

Well for one thing, it wasn't just "one big battle" from one end to the other. There was such a thing as a quiet sector, as the research of Tony Ashworth in the late 1970s showed, and while there might be trench raids, spoiling attacks and localized operations, for the most part fighting was confined to the large offensives launched from 1915 onwards.

As to definitions, Offensive was most often used to describe a major operation, such as the 1st/2nd/3rd Artois Offensives, 1st/2nd/3rd Champagne Offensives, the Somme Offensive, the Nivelle Offensive & the Arras Offensive, the Flanders Offensive (the 3rd Battle of Ypres), etc. Sometimes Operation might be used in accounts interchangeably with Offensive, such as Operation Gericht (the Verdun Offensive), Operations Michael/Georgette/Mars/Gneisenau/Blucher-Yorck (the Spring Offensives), etc.

The term 'Battle' could be and was used to describe all of the offensives/operations I listed above, more often than not as a colloquialism. This creates the odd situation of having battles within a 'battle,' such as the Battle of Albert during the Battle of the Somme, or the Battle of Pilckem Ridge during the 3rd Battle of Ypres. As I just said, the term 'Battle' should be treated loosely, as it was more of a colloquialism than a descriptor in the case of the larger offensives/operations/campaigns etc., call them what you will.