Health
Okay this one is pretty straight forward. The more health you have, the more damage you can take before dying. Simple.
There are a few abilities in the game that cost health to cast, and a few abilities or item set 'procs' that scale off of maximum health. These are mostly for niche builds though.

Stamina & Magicka
Stamina and Magicka are used as resource to cast their respective abilities. Simple enough! Stamina is also used to Roll-Dodge, Sprint, and Block with ordinary weapons, while magicka is used to block with a Frost Staff.
The highest of your Magicka or Stamina ("Primary Resource"), however, will affect your character unique ways:

1. Some Synergies restore more of your primary resource. For instance, the Spear Shards synergy (from Templars) restores twice as much primary resource as it does the secondary.
2. Many item set 'procs' scale with the higher of your Stamina or Magicka.
3. Your max resource affects your character's Effective Power - namely, every 10.5 points of max. Stamina or Magicka is equivalent to +1 Weapon/Spell Damage.
   A character with e.g. 30,000 Max Stamina gets 2857 additional effective power.

Every 660 points of Physical Resistance reduces your damage taken from Martial Attacks by 1%.
Every 660 points of Spell Resistance reduces your damage taken from Magical Attacks by 1%.

Aside from a handful of buffs, your character's Physical and Spell Resistance comes from the choice of armor you're wearing.
Armor values follow the same standard values determine by weight (light, medium, or heavy) and which body piece it is.
It is, of course, obvious that A less obvious fact is that body pieces are rated as; In addition, there are Passive Bonuses and/or weaknesses associated with each type. For example, each piece of Heavy Armor reduces Spell Resistance by 1%, but buffs resistance to Martial attacks, and vice versa for Light Armor.

One last thing should be noted w.r.t. armor weights. The Undaunted skill-line Passive, Undaunted Mettle, grants +2% bonus to your Main Attributes per different armor weight worn. Meaning that you get from 2% when wearing only one type, up to 6% if you wear at least one piece of each armor weight. If you've seen terminology like 5M/1H/1L it refers to a distribution of 5 Medium, 1 Heavy, 1 Light pieces to optimize attributes.

Critical Resistance
Every 66 points of Critical Resistance reduces Critical Damage taken by 1%

As Monsters cannot critically hit, Critical Resistance is exclusively a PVP-stat, useful for trolling Nightblades reducing enemy burst potential.

Weapon/Spell Damage
Admittedly the name of this section is a bit inaccurate - but in my defense, that's because the game itself has increasingly inaccurately named stats.
The higher of your Weapon or Spell Damage will determine the damage (and healing) of all abilites.

Since High Isle, Weapon and Spell Damage from item sets always come together. There are very few sources left in the game, which do not give both.
Your Weapon and Spell Damage are increased by Brutality and Sorcery buffs, respectively. Again; most sources of Major Sorcery/Brutality also includes the other, but potions are an exception to this rule! Make sure you use either Brutality Potion or Sorcery potions, depending on which stat you're maximizing.

P.s.
For Dragonknights, it is advisable to stack Weapon Damage, as the Mountain's Blessing passive gives access to Minor Brutality, increasing WD by 10%.
For Templars, the Illuminate passive yields Minor Sorcery, increasing SD by 10%.

Critical Chance
Every 219 points of Critical Rating increases chance to critically strike by 1%.
Much like Weapon/Spell Damage, chance to crit is determined by the higher of your Weapon or Spell crit.

A critical strike deals 50% additional damage, making critical chance one of the highest yield offensive stats.
This damage modifier may be further increased by stacking Critical Damage.

Critical Damage
Similar to Critical Chance, this is another very strong stat. It acts much like Critical Chance for modifying damage, but is a much rarer stat in terms of item set bonuses.
Critical Damage bonus added on top of the base 150% modifier, so +10% Critical Damage from e.g. Minor Force buff pushes your crits to a 160%=1.6x multiplier.

Critical Damage is capped at 125% Bonus (for a total of for 225% of normal Damage), but this is rather hard to achieve outside of organized Trial Groups (though not impossible...).
Generally you want to prioritize Crit Chance over Crit Damage, but a lot of sources provide both any way, e.g. Order's Wrath Set, Harpooner's Wading Kilt, etc.

Offensive Penetration
As mentioned in Resistances, every 660 points of Physical or Spell Resistance reduces the incoming damage by 1%. This means that every 660 points of Offensive Penetration increases your damage dealt by 1% as long as the opponent has Resistance left to penetrate.

Monsters in ESO have a baseline 9200 (overland) or 18200 (Group content) Resistance - but be wary! there is no benefit to 'overpenetrating' - overshooting the mark does not yield extra damage.
Thus, Penetration is mostly prioritized in PVP or for solo/small-scale PVE. Larger Trial Groups of 12 people will often have enough debuffs running that enemies are essentially down to 0 Resistances any way.

That being said; if you're running solo, or in less optimized groups, Penetration remains the single highest damage stat, line for line.

• Abilities scale with the higher of your Weapon or Spell Damage.
• Every 10.5 points of max resource (stamina or magicka) have the effect of +1 Weapon/Spell Damage
• 219 Critical Rating = 1% Critical Hit chance
• Critical Hit = 150% of base damage, up to 225% with bonus Critical Damage
• Every 66 Points of Critical Resistance reduce Critical Damage taken by 1%
• Every 660 Points of Resistance reduces incoming damage by 1% /// Every 660 points of Penetration increases damage by 1%.
• Gear armor values are: Chest > Helmet/Shoulders/Legs/Sabatons > Gauntlets > Belt