Ok, this is a big one. There are a lot of stats in the game. Let's start with the basic 3 - strength, ability, and tactics.
Strength effects your survivability. So, health, protection, defense. Tanks usually have this stat the highest.
Agility effects physical damage. If your character inflicts that kind of damage with one or more of his attacks (most do), this stat is so important.
Tactics effect special damage & resistance (armor against special damage). This stat is usually high in support toons, as well as toons that inflict special damage only (EP, Nihilus, Krennic).
Defense is a stat that effect your armor and resistance. The higher it is, the less damage you'll take from attacks.
Offense effects both physical and special damage.
Armor penetration reduces the armor of the defending toon. This stat is more important against some toons than others.
Speed is the rate your TM bar fills naturally. If, your example, 1 toon has 300 sure and another has 200, the first toon will go 1st, use his ability, and start refilling. When he'll reach 50%, the 2nd ton shall have his filled and take his turn.
TM gain gives you a one time boost to the TM. In the same way, TM reduction gives you a penelty. None effect your speed, just the amount there's saved up.
Health and protection do not effect one another. The rate is different between each toon.