Different units have different types of armor. Heroes have Hero armor. Creeps have Basic armor. Buildings have Structure armor. Likewise, each unit has a type of attack damage. For example, heroes deal Hero damage.

Depending on the type of attack damage being dealt and the type of armor the target has, the damage can be increased or decreased by a multiplier. If it it Hero damage versus Hero armor or Basic armor, the multiplier is x1, so it does as much damage as you would expect.

The armor number a unit shows decreases incoming damage more and more as the armor number goes up. So the armor number is effectively another multiplier. Thus, the damage a unit receives is based off the damage type, the armor type, and the armor number.

In the case of cleave, only Heroes and creeps can be hurt by it. Both groups' armor neither increase nor decrease damage taken from a Hero. So, the armor type does not matter when dealing with cleave.

Cleave also ignores the armor number. This means that any unit hit with cleave will always take damage equal to the cleave percent multiplied by the damage the main attack target took, regardless of the cleaved upon unit's armor.

That line in the Battle Fury description essentially doesn't matter. It used to matter because there used to be a few more armor types and some of them would have reduced the cleave damage. However, those armor types no longer exist, so that line is just a relic of the past.

You can read more about armor here:

http://dota2.gamepedia.com/Armor

tl;dr it doesnt matter