Packet usually refers to one of two things in the context of Guild Wars: a network packet between the player's computer and the game server or a packet of health/energy increase or decrease. The former is a complicated subject that does not relate specifically to Guild Wars.
Within Guild Wars, a packet is a single number displayed on the screen that represents health or energy loss or gain. The final result of packets is always the same no matter how many there are, but the number of packets can affect how different skills interact. Generally, skills which perform operations on damage perform it on each packet, rather than operating on each skill.
The most prominent examples of separate packets are damage over time area of effect skills, which deal large amounts of damage in smaller packets. Each packet is counted as a single hit, not tallied together as the effect of one skill. The number of packets a skill produces can affect the effectiveness of various skills, particularly Protection Prayers skills. For instance, Fire Storm cast at 15 Fire Magic would produce a rain of fire that deals a total of 350 damage (before armor), but arrives in ten 35-damage packets. Against a basic 480-health character who can't or won't leave the storm, it would deal 350 damage. If that character was enchanted with Protective Spirit, the damage wouldn't be reduced at all, but Shielding Hands would (at 15 Protection Prayers) reduce it by a total of 180, more than cutting it in half (assuming the duration of the enchantment was extended to last the full 10 seconds necessary). On the other hand, Shielding Hands would only reduce the damage from Rodgort's Invocation from 120 to 108, but Protective Spirit would reduce it from 120 to 48.
Some skills that deal both damage and additional damage will deal the additional damage in a separate packet. For instance, Shockwave cast at 15 Earth Magic while adjacent to a foe will deal a total of 180 damage (before armor), but arrives in three 60-damage packets. If the foe was enchanted with Reversal of Fortune at 15 Protection Prayers, one of the three damage packets would be reduced to 0, that foe would be healed for 60, and receive 120 damage. On the other hand, Teinai's Wind cast at 15 Air Magic will deal a total of 120 damage (before armor) on burning foes, but arrives in one packet. If a burning foe was enchanted with Reversal of Fortune, that foe would be healed for 80 and receive 40 damage.
Packets influence offensive spells as well: Barbs, for instance, triggers for each packet of physical damage the hexed target takes, even if it's from the same skill (e.g. Dual Shot) or attack (e.g. double strike).
Packets come in both health and energy forms, but packets of energy do not have any effect on gameplay because there are no skills which take energy packets into consideration.
Skills that deal both damage and additional damage
In separate packets
|Aftershock||Spell. Deals 26...85...100 earth damage to nearby foes. Deals 10...56...68 more earth damage to knocked down foes.||10||¾||10||Earth MagicZ||Core|
|Jungle Strike||Off-Hand Attack. Deals +10...22...25 damage. Deals +1...25...31 damage to target and adjacent foes if target foe is Crippled. Must follow a lead attack.||5||½||10||Dagger MasteryZ||Factions|
|Lightning Bolt||Spell. Projectile: deals 5...41...50 lightning damage. Deals 5...41...50 more lightning damage if target foe is moving. 25% armor penetration.||5||1||8||Air MagicZ||Nightfall|
|Mind Burn||Elite Spell. Deals 15...51...60 fire damage. If you have more energy than target foe, deals 15...51...60 more fire damage and inflicts Burning (1...8...10 second[s]). Also hits adjacent foes.||5||5||1||5||Fire MagicZ||Core|
|Mind Freeze||Elite Hex Spell. Deals 10...50...60 cold damage. If you have more Energy than target foe, deals +10...50...60 cold damage and causes 90% slower movement (1...4...5 second[s]).||5||5||1||5||Water MagicZ||Core|
|Mind Freeze (PvP)||Elite Hex Spell. Deals 10...34...40 cold damage. If you have more Energy than target foe, deals +10...34...40 cold damage and causes 90% slower movement (1...4...5 second[s]).||5||10||1||5||Water MagicZ||Core|
|Shockwave||Elite Spell. Foes in the area take 15...51...60 earth damage and are Weakened (1...8...10 second[s]). Nearby foes also take +15...51...60 earth damage and have Cracked Armor (1...8...10 second[s]). Adjacent foes also take +15...51...60 earth damage and are Blinded (1...8...10 second[s]).||10||1||15||Earth MagicZ||Factions|
|Spear of Light||Spell. Projectile: deals 26...50...56 holy damage. Deals 15...51...60 more damage if target foe is attacking.||5||1||15||Smiting PrayersZ||Factions|
|Teinai's Crystals||Spell. Deals 20...36...40 damage to target. Deals +20...36...40 more [sic] damage and causes Cracked Armor (5...13...15 seconds) nearby if that foe had a Water Magic hex.||5||1||8||Earth MagicZ||Factions|
In the same packet
|Blinding Surge||Elite Spell. Deals 5...41...50 lightning damage. Inflicts Blindness condition (3...7...8 seconds) on target and adjacent foes. 25% armor penetration. If target was attacking, also hits adjacent foes and deals 50% more damage.||10||¾||6||Air MagicZ||Nightfall|
|Sandstorm||Elite Spell. Deals 10...26...30 earth damage each second (10 seconds). Hits foes near target foe's initial location. Hits attacking foes for 10...26...30 more earth damage each second.||15||2||25||Earth MagicZ||Nightfall|
|Smite||Spell. Deals 10...46...55 holy damage. Deals 10...30...35 more holy damage if target is attacking.||10||1||10||Smiting PrayersZ||Prophecies|
|Teinai's Wind||Spell. Deals 10...34...40 cold damage. Burning foes take +40...72...80 damage and are interrupted. Also strikes adjacent.||5||1||8||Air MagicZ||Factions|