What is true damage?

Changelog of patch 1.0.0.111 reported:

Smite now deals true damage instead of magic damage.

What does true damage mean and how does it differ from magic/attack damage?

Solution 1:

True damage does exactly the listed damage, as True Damage is not reduced by armor or magic resistance, nor by any flat or %reduction granted by champion abilities.

In the past, true damage was subject to the same multiplicative modifiers as magical or physical damage -- i.e., doing more on a Hemoplague'd target, less on Alistar's Unbreakable will, etc., however it appears that Riot considers this a bug, as they have been slowly "fixing" true damage dealing reduced effect to Olaf's Ragnarok, or while under Sona's Diminuendo debuff (for example).

The reason this change was made is because smite used to do magic damage, where it was particularly effective against the jungle creeps (who had negative magic resistance, and thus took extra damage from smite). Recently, the mobs were patched to have non-negative magic resistances, so smite lost effectiveness, even though ability itself wasn't changed.

Solution 2:

True damage ignores armour/ resistance. It is similar to chaos damage in Warcraft3.