One of the two main weapon damage types, energy damage is more commonly used by ranged weapons than by melee weapons. All lightsabers apply energy damage. Reconnaissance armor tends to have more protection to energy damage than battle armor, while assault armor will have less protecion. Personal shield generators can absorb energy damage only.
When choosing a weapon for a particular situation, the type of damage it will deliver is of importance. Since armor cannot be changed while in combat, switching damage types can be an effective way to improve your chances.
Other than having different protection values, there is no difference in effects between the two main damage types.