Physical damage is dealt by all basic attacks, by some hero abilities and by some item effects.
Most physical damage is based on the hero's attack damage (but not all damage based on attack damage does physical damage). The physical basic attack damage is increased by attack speed, critical strike and armor penetration or reduction. A small number of hero abilities that deal physical damage can be strengthened with ability power.
Not all physical damage sources proc life steal, but most that apply on-hit effects do.
The amount of physical damage received is reduced by a certain percentage based on the target's armor or other damage reducing effects. The effectiveness of armor can be reduced with armor penetration or reduction.
Magic damage is dealt by some items and most heroes' abilities, though some abilities deal physical or true damage.
Most magic damage can be increased with Ability Power, or Attack Damage in some rare cases, but some cannot be modified, such as Searing Armor's damage per second or Energy Absorbing Sword's active against heroes.
The amount of magic damage received is reduced by a certain percentage based on the target's magic resistance or other damage reducing effects. The effectiveness of magic resistance can be reduced with magic penetration or reduction.
True damage ignores armor and magic resistance, but doesn't ignore damage reduction.
Despite popular belief, heroes whose abilities have health costs associated with them do not deal true damage to themselves when they use an ability which requires health to cast.
This can be evidenced when they have an absorption shield on them, when they use their health-based ability, the cost of it penetrates the shield and directly drains the health of the user, in contrary to true damage that has to break any absorption shield on the target to reach its hitpoints.
True damage is also unaffected by damage amplification in the Hero Stats.