What is chaos damage in Path of Exile?

Chaos damage is poison in some cases, but not always. Chaos damage ignores armour, elemental resistances and energy shield. The only way so far to have resistance (in this case immunity) to chaos damage is by getting Chaos Inoculation from passive skills tree. If you have high evasion you can dodge some chaos attacks (like the "Viper Strike").

With the release of Open Beta, several forms of chaos resistance now exist in addition to Chaos Inoculation, including several nodes, armor affixes, and chaos resistance flasks.

Sources: Official forum , PoE wiki

It bypasses energy shield, not resistances. If you have chaos resistance, you will take less damage from it, but I haven't seen a single chaos resistance item dropped yet, as of Act 3. However, you can get chaos resistance from a skill list.