Constitution - Adds 8 max points to your Health Bar and 2 max points to your Action bar for every 1 point.
Stamina - Adds 8 max points to your Action bar and 2 max points to your Health bar for every 1 point.
Precision - When you are using a ranged weapon, your Precision and Offence is checked against your targets Agility and Defense stats. If your Precision + Offence is greater than your targets Agility + Defense then your minimum damage is increased. So If you normally do 10 to 90 points of damage per hit, you would do 50 to 90 points of damage per hit instead.
Strength - When you are using a melee weapon, your Strength and Offence is checked against your targets Agility and Defense stats. If your Precision + Offence is greater than your targets Agility + Defense then your minimum damage is increased. So If you normally do 10 to 90 points of damage per hit, you would do 50 to 90 points of damage per hit instead.
Agility - If your Agility + Defense is higher than your attackers Strength or Precision + Offence then their maximum damage will be lowered. So if you would normally get hit for 10 to 90 damage per hit, you would be hit for 10 to 50 points of damage per hit instead.
* The effects of Strength, Precision and Agility are currently too subtle and will be modified in the future these so that they're more important and more obvious.
Luck - The <<LUCKY!>> message in the combat fly text means you scored a critical hit. You'll notice that you hit for two times or more of your normal damage, this also works with heals in that you will heal for more damage. This is also reported to work in space combat, crafting and selling junk to junk dealers.
Offence - this stat increases when Jedi's "Vapad Focus" buff is used. Combines with your Precision and Strength stats (see above).
Defense - this stat increases when Jedi's "Soresu Stance" or Officer's "Stratagem" (group buff) is used. Combines with your agility stats (see above).
Damage - an indication of the damage you will output with your chosen weapon.
Kinetic, Energy, Heat, Cold, Acid and Electricity - Sum of the protection given to you by armor.
Miss
NPCs and players with ranged weapons in Auto-Aim mode have a base 5% chance to miss their target. Factors such as debuffs and movement increase the player's chance to miss. Buffs and the strength stat reduce the chance to miss.
The base miss chance for melee and ranged in Manual-Aim mode is 0%.
Dodge
Dodge is a defender attribute that gives a chance to avoid incoming damage. On a successful roll, the attack will be treated as a miss and no damage will be applied.
Block
Block is a defender attribute that has a chance to mitigate additional damage based on the defender's block score. Block mitigation is applied after armor so it is possible to reduce incoming damage to 0 with a high enough Block Value.
(Block Value + Strength) / 2 + 25 = Block Value
Parry
Parry is a melee defender attribute that will allow the defender to negate a successful attack. Normal parry can only block other melee attacks though Lightsaber weapons can parry ranged attacks as well.
Strikethrough
Strikethrough is a type of critical which instead of adding damage will bypass a % of your target's armor. Strikethrough amount is based on the attacker's Strikethrough Value.
Evasion
Evasion is a defender attribute that will allow the target to avoid a % of damage from an Area Effect attack. The amount of % evaded is determined by the defender's Evasion Value.
Punishing Blow
A punishing blow is a type of critical only available to NPCs that do 150% damage. Elite and Boss category NPCs (as well as those higher level than the player), can land a punishing blow.
Glancing Blows
The damage reduction from a glancing blow has been reduced from 96% to 60%. In addition, Elite and Boss category NPCs (as well as those higher level than the player), have a natural chance to receive a glancing blow
Thanks again for the explanation given in guildchat and now also here, but I have to point out that it doesn't work exactly as described.
I tried to switch some items that I was wearing and nothing changed on my HP or AP. It seems that the improvements are not given for each single point, but just when your attribute is higher than a set of thresholds. I mean that if your constitution is 54 and you wear a ring that gives you 5 more points, you do not see any effects. Nevertheless it could also happen that if you wear another item that gives you 5 more points, you can see the changes on HP and AP. The number I gave are purely hypothetical, I will investigate more on this and send an update if I find out something more consistent.
Now with Pub 27 everything seems fixed. Each time I wear an object which gives const or stamina bonus, I see the changes in HP and AP as Alastrina explained.