Stats

Primary Stats

• Bravery means that a soldier may keep his wits even when Morale drops. If you need this, something probably went very very wrong.
• Reactions determine a soldier's ability to shoot first when stumbling upon an enemy, and vice versa. Very important.
• Firing Accuracy should need no explanation. Probably the most important stat of all.
• Throwing Accuracy the importance of this trait depends on your play style. Most players don't worry too much about it.
• M.C. or Psionic Skill: the ability to mind control aliens, once the prerequisite technology is available. Also adds a small bonus to a unit's mental defences.

Reactions and Firing Accuracy are probably the most important stats to look for when hiring new soldiers. Not only are these skills crucial in combat, they also require success in order to improve: a bad marksman who never hits will also never gain Experience, while a soldier who has a high Firing Accuracy to begin with will improve on this ability with relative ease. The same is true for reactions.

Training setups to improve any single or even several skills are possible (see the respective main articles as well as Experience Training) but are either difficult, risky, tedious or any combination thereof.

Secondary Stats

• Time Units determines mostly how far your Soldiers / Aquanauts can advance each turn (although there's more to it). Not exactly vital, but very convenient.
• Energy or Stamina determines how far your soldiers can run until they run out of breath. Hardly ever matters.
• Health – A soldier with high health may survive an otherwise deadly hit, the percentage of remaining health influences firing and throwing accuracy. Sounds important, but really doesn't make much of a difference.
• Strength, unsurprisingly, determines how much a soldier can carry until she's bogged down by the weight of her gear. Vital when it comes to carrying much or heavy equipment. Also determines how far an object of certain weights (like grenades) can be thrown.
• M.C. or Psionic Strength: the ability to withstand alien mind control attempts. Will never improve.

Secondary stats are not tied to specific actions and will improve almost automatically (with the exception of Psi/MC Strength, of course). The worse they are to begin with, the faster the increase. So there is no need to sack a weak or slow soldier: provided they can make themselves useful, they will catch up within just a few battles.

Combat Stats

• Energy recharge. How much energy the unit will recharge per turn. For X-Com soldiers, this stat is derived from their base Time Units and remains fixed for the rest of the game. Aliens and HWPs have particular values assigned to them.
• Fatal Wounds may be incurred when hit. A soldier with fatal wounds will take damage every turn until either: a) she dies, b) the wound is treated, or c) the battle ends.
• Morale changes over the course of a battle, depending (mostly) on how well your team fares. If it drops below 50, the soldier will have to pass a bravery check.