Auto Attacks & Armor Types
- Heroes do 100% to all units other than tower (which they do 50% to)
- Most units do less to towers, but Siege will do 150%
Armor type is something built into units. All heroes are Hero Type.
Damage Types
- Physical - auto attacks, and some abilities (e.g.
Slardar's stun)
- Magical - most spells
- Composite - reduced by armor and magic resist, but not blocked by anything (e.g.
Beastmaster's 
Wild Axes, 
Leshrac's 
Diabolic Edict)
- HP Removal - directly removes HP, does not stop stuff like
Healing Salve healing (e.g. 
Necronomicon aura)
- Pure - not reduced by anything, but blocked/cannot target Magic Immune (e.g.
Silencer's Glaives)
- Universal - not blocked by anything, but magic resist works on it (e.g.
Doom's 
Doom, 
Tinker 
March)
Modifiers
You can modify yourself or others in various ways too:
- Ethereal - done with stuff like
Ghost Scepter or 
Ethereal Blade, as well as 
Pugna's Decrepify. You'll take bonus magic damage, but are immune to physical.
- Magic Armor - items like
Pipe of Insight, 
Hood of Defiance, etc. will buff it up. Most heroes have 25% magic resist (exceptions being like 
Visage who has 10%, or 
Meepo who has more)
- Magic Amp - items like
Veil of Discord increase magic damage taken
- Magic Immune -
Black King Bar makes you immune to magic, as does stuff like 
Lifestealer's 
Rage ability
- Magic Abosrb - items like Pipe can be activated to provide a buffer that absorbs some magic damage. Similarly,
Ember Spirit has an ability that basically does that.
- Armor Reduction - you can get something like
Desolator to reduce another hero's armor
More info at Dota2 gamepedia
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