Cleave causes a melee unit's attacks to deal a portion of their damage in an AoE. The damage dealt by Cleave is reduced by armor type, but not by armor value, and derived from the actual damage of the attacking unit (as opposed to the damage that the primary target took from the attack). Cleave does not affect the primary target of the attack.

Cleave does not extend the effects of most orbs/buff placers you may have. If you have a Stygian Desolator and a source of Cleave and you attack a unit, only the main target of your attack will receive the Corruption buff from Stygian Desolator. The only buff placer that affects Cleave is Critical Strike. If you proc a Critical Strike when you cleave, the damage multiplier will affect all units hit by the Cleave.

Multiple sources of Cleave work completely independently from each other. If you have a 500 AoE 50% Cleave, and a 250 AoE 35% Cleave, you will deal 50% of your damage in 500 AoE, and 35% of your damage in 250 AoE. Each Cleave source causes another instance of damage for the affected units.

Cleave AoE is a circle with radius equal to the Cleave range, and its center at a distance equal to the Cleave away from the attacking unit, towards the primary target of the attack.

Here is a picture to clarify:
(units within the yellow circle would be affected by a Cleave with radius equal to the length of the yellow line)


Cleave in DotA

There are several sources of Cleave in DotA, they are listed below.

Battle Fury

Magnitude: 35%
Radius: 225

Rogue Knight - Great Cleave

Magnitude: 20%/30/40%/50%
Radius: 175

Magnataur - Empower

Magnitude: 15%/25%/35%/45%
Radius: 200

Admiral - Tidebringer

Magnitude: 100%
Radius: 380/420/460/500

Tiny - Warclub

Magnitude: 50%
Radius: 400