Attack and Defense is a core concept in SMITE.
Damage
Damage is what attacks and offensive abilities cause on enemy targets. Damage deducts health from the affected target. If a unit loses all of their health they will die, rendering them unable to continue fighting.
There are three types of damage in the game: Physical, Magical, and True damage. Gods are classified as being either magical or physical, with their attacks and abilities applying the matching type of damage. Physical damage can be mitigated by physical protection, and magical damage can be mitigated by magical protection. True damage deals its full amount regardless of how much physical or magical protection the target has. True damage is relatively rare; an example is Bakasura's Butcher Blades ability.
Damage reduction is a mechanic that reduces the damage output of the afflicted god or unit. It can either affect a single type of damage or it can affect all types of damage, including True damage. The inverse of this is damage increase, which will boost damage dealt with one or any type of damage. For example, Shaman's Ring increases all damage the affected target takes from the user.
There are rare circumstances where gods can apply damage of a different power type than their own. For example, 
Mystical Mail has an aura effect that deals magical damage around the user and can be acquired by physical gods.
Power
Gods have a "Power" statistic which attacks and abilities scale from, increasing their damage output. Most gods start with 0 power (an example of an exception is Kukulkan whose passive ability grants him magical power equal to a percentage of his maximum mana) and can gain power from items and some god ability effects. Certain jungle buffs can also increase a god's power.
Basic Attacks
Basic attacks scale based on the god's level and their Power stat. The "Basic Attack" number indicates the amount of unmitigated damage a basic attack does. Each god has a formula that defines what their Basic Attack value is. The formula for how basic damage is calculated is:
Base Damage + (Base Damage per lvl × God's lvl) + (100% of Physical Power OR 20% of Magical Power)
All magical gods scale at 20% of their Magical Power, and all physical gods scale at 100% of their Physical Power. For example, Agni's basic attack damage is 34 + 1.5 × level + 20% of Magical Power. Izanami is the only exception to this rule; she is a hunter who has boomerang like basic attacks which can go through multiple targets and that scale at 75% Physical Power when fired and 25% while they are returning to her.
Buffs and effects that grant a percentage basic attack damage increase will apply the bonus before the physical/magical power contribution.
Attack Speed defines how many attacks a god can fire per second. The higher the value is, the sooner a god will be able to reuse their basic attacks.
Some gods have a hit progression which affects the swing time (the delay before a basic attack is actually fired) and amount of damage a basic attack does, and in some cases even granting them an additional effect. A good example of this is Ne Zha, who has a 4 stage basic attack progression where the first two attacks deal 100% damage with normal swing time, while the third attack has a 150% damage and swing time, finishing with a 200% damage and swing time attack that affects an AoE in front of him.
Physical gods have access to Critical Chance, which gives them a chance to land critical strikes with their basic attacks. Critical strikes deal 200% (twice) as much damage as a regular basic attack. The item 
Deathbringer increases how much damage critical strikes do by an extra 30% (230% total).
Launching a Basic Attack while moving will apply a movement penalty that reduce movement speed by 50% for ranged gods and 35% for melee gods (The movement speed counter will not change while doing so). The "Haste" passive effect of items such as 
Hastened Katana and 
Hastened Ring removes this movement penalty on activation.
Abilities
Most damaging abilities have a base amount of damage (which may increase each time a point is put into the ability), plus an additional amount based on the god's Power stat. For example, Ra's Celestial Beam at max rank will do (335 + 90% of Magical Power) unmitigated damage. Some abilies may also scale with Basic Attack Power, which is equal to the damage the god currently deals with their basic attacks.
There are a few abilities in the game, like Mercury's Made You Look and Ne Zha's Armillary Sash, that can be affected by Critical Chance, which is normally something that only affects basic attacks.
Protections and Mitigation
Protections and mitigation alleviate the impact of incoming enemy attacks and abilities on the victim's health, which can prevent (or at least delay) their death.
A god's magical and physical protection values will reduce the amount of damage the corresponding types of damage apply. A god's inherent protections scale with level. For example, Ymir's total physical protection is 23 + 3.3 × level + Physical Protection From Items. Ignoring penetration for now, the formula for how a protection value reduces damage is:
Damage = (100 × Unmitigated Damage)/(Protections + 100)
The result of this equation means that a protection value of 50 will reduce damage by 33%, 100 will reduce it by 50%, and 150 will reduce it by 60%.
For example (still ignoring penetration), if Ra's Celestial Beam is listed as doing 335 damage, and he hits someone with 70 magical protection, then the actual damage will be 197 = ((100 × 335)/(70 + 100)).
Damage can also be mitigated by percentage damage reduction like Athena's Defender of Olympus. Percentage damage reduction can't be penetrated by any means and, unless otherwise stated, will affect even True damage.
Some abilities and items, like Geb's Hard as Rock passive or 
Spectral Armor, can lower the amount of extra damage dealt by critical strikes.
Penetration and Reduction
Penetration and reduction help counter an enemy's defenses, increasing the efficiency of attacks and offensive abilities.
A target's protection values can be lowered or bypassed with certain items and abilities that grant penetration and reduction effects. They are (in order):
- Percent Reduction. This will reduce a target's protection values by a percentage. For example,
The Executioner will reduce a target's physical protection by 12% (per stack). - Flat Reduction. This will reduce a target's protection values by a specific amount. For example, Void Shield will reduce a target's physical protection by 20.
- Percent Penetration. This will ignore a target's protection values by a percentage. For example, Titan's Bane will ignore 15-45% of a target's physical protection.
- Flat Penetration. This will ignore a target's protection values by a specific amount. For example, The Crusher will ignore 15 of a target's physical protection.
Thus, to determine the actual protection values of a target, the equation is:
Actual Defense = (Protection × (1-%Reduction) - Flat Reduction) × (1-%Pen) - Flat Pen
Flat penetration is capped at 50. The protection values cannot go below zero.
Example
An example of a highly unlikely build for a Mage is:
- Demonic Grip: +12% Reduction per stack
- Void Stone: -15 Protections
- Obsidian Shard: +15-45% Penetration
- Dynasty Plate Helm: +10 Penetration
This mage has a Basic Attack value of 105. Fighting against an opponent with 238 magical protections, the first basic attack will do:
Actual Defense = (238 × (1-0) - 15) × (1-.45) - 10 = 112.65 Actual Damage = (100 × 105) / (112.65 + 100) = 49
Now that a Demonic Grip stack is applied, the next basic attack will do:
Actual Defense = (238 × (1-.12) - 15) × (1-.45) - 10 = 96.94 Actual Damage = (100 × 105) / (96.94 + 100) = 53
And the next basic attack now with 2 Demonic Grip stacks:
Actual Defense = (238 × (1-.24) - 15) × (1-.45) - 10 = 81.23 Actual Damage = (100 × 105) / (81.23 + 100) = 58
And the final basic attack now with 3 Demonic Grip stacks:
Actual Defense = (238 × (1-.36) - 15) × (1-.45) - 10 = 65.53 Actual Damage = (100 × 105) / (65.53 + 100) = 63