Effect damage is any damage that is not caused by battle (with the exception of "Gravekeeper's Vassal") or is a reduction. Examples of cards that cause effect damage are "Poison Mummy", "Ookazi", "Ancient Gear Gadjiltron Dragon (If "Yellow" or "Red Gadget" are Tributed) and "Ceasefire".
Costs are not considered effect damage, such as with cards like "Injection Fairy Lily" and "Dimension Fusion". Damage from Monster Cards with "Piercing" effects are considered Battle Damage. Key words to look out for on cards that deal effect damage are "Inflict" and "Direct Damage". If it says "Pay" it is a cost. For example, "Archfiend" monsters do not deal burn damage to their user, but instead lower their Life Points as a cost.
Some cards are capable of lowering a player's Life Points without technically inflicting battle/effect damage. Prime examples are "Destiny HERO - Dogma" and "Life Equalizer". These cards can be particularly troublesome because they are unaffected by cards such as "Cyber Kirin" and "Rainbow Life", as those cards deal specifically with damage.
Some cards that are specifically designed to work with Direct Damage are "Barrel Behind the Door" and "Trap of Board Eraser". You can combine these with cards that deal Burn Damage to you such as "Granadora" and instead reflect it back to your opponent as damage or as a nasty effect. However, be sure to remember the distinction between "Damage" and "Life Loss" when dealing with these cards ("The Immortal of Thunder", for example, causes Life Loss, not Damage, so you cannot combine it with "Barrel Behind the Door").