Spell Damage affects only cards that are of type Spell - they have a "Spell" label sticked to the bottom of the card, when you hover your mouse over it.
There are three types of cards in Hearthstone:
Traps, or more precisely Secrets, are Spells and are affected by Spell Damage, but in a slightly different way than usual. The bonus to damage dealt by Secrets is applied when it triggers, and not when it is being cast.
There are a couple visual cues in game that let you see which cards get affected by Spell Damage:
- When you have a minion with +Spell Damage on the table, all the spells in your hand that deal some damage display the number of damage already increased by all the +Spell Damage effects currently active. Additionally the number is surrounded by asterisk (*).
- When you hover your mouse over your minion with +Spell Damage on your battlefield, all the cards in your hand, that are affected by the effect, get highlighted with a purplish glitter for a few seconds.