Composite damage was a mechanic where damage could be both physical and magical, and both armor, damage block and magic resistance applied to it, but it could damage magic-immune target, but does not affect ethereal units.
Composite damage will be removed in Dota2 patch 6.82. The heroes that had composite damage abilities prior to that patch included:
Leshrac - Diabolic Edict (changing to Physical)
Beastmaster - Wild Axes (changing to Physical)
Alchemist - Acid Spray (changing to Physical)
Techies - Land Mine (changing to Physical)
Lone Druid - Backlash upon death of Bear (changing to HP Removal)
... and HP Removal is no longer a "Damage Type", but a side-effect of using certain hero abilities (e.g. Huskar Burning Spears).
From the dota2 wiki:
** Composite damage is calculated by multiplying the initial
damage by the target's magic resistance and armor. For example, if you
had 25% magic resistance, 50% physical damage resistance, and stepped on
a full damage Level 4 Land Mine, the equation would be 600 x 0.75 x
0.50 = 225 actual damage. (Magic resistance and physical damage
resistance percentages are subtracted from 100%.)