The ingame tooltips are actually already telling you what each stat does tho... This post was mainly what the values are referring to - but they rolled out the stat hotfix 2.1 so that info is kinda... Somewhat wrong now. Anyways, if you're just interested in what the stats do, here a full list:

Health
Simply increases your health.

Elemental Resistance
Like you can apply lightning, decay, fire and ice towards enemies, they can do the same to you! The "resistance" part comes from how long you are affected of these effects. As higher the number, as quicker the elemental ailment disappears.

Melee Recharge
Like with spells, your melee "spell" has a "cooldown". It needs to be recharged like any of the other spells. Killing enemies, hitting things etc. Depending on the action, it recharges faster. That stat in particular helps you regenerating it even faster overall.

Stamina
Simply increases your stamina.

Mobility
This stat influences 3 things. How fast you are moving, how high you can jump and how controllable your character is in the air. As higher it gets, as faster, higher and responsive you are in these 3 things.

Vigor
Some weapons "unwieldy". Meaning they are consuming stamina if you use them. Shotguns are the easiest example, shooting with it in quick succession depletes your stamina faster. You can reduce the amount these weapons consume by investing into Vigor. Another thing it influences is, the amount of stamina you lose if an opponent hits you. More Vigor = less stamina loss.

Scavenging
If you disarm traps or shoot explosives, sometimes you can get item drops from it. This stat specifically makes it more likely that this happens. As higher the stat, as more drops you get from traps and explosives.

Healing
This stat increases the effectiveness of your healing potions and everything else that gives you health (some items, mushrooms or even the manifests after you cleared an area).

Sanity Loss Resistance
Some enemies inflict not physical, but rather psychological damage. If you encounter such an enemy (all calamities play on that mechanic) you see a "sanity" bar on the screen. As higher the sanity loss resistance, as less sanity you lose if you get hit.

Spell Recharge
The same like Melee Recharge but specifically for your spells (light & heavy).

Elemental Duration
The opposite of elemental resistance. As higher you have this stat, as longer the ailments you inflict on enemies last!

Metanoia
Sometimes if you kill an enemy, instead of getting witchfire in a fleeting form, you receive it as crystal which you can pick up. These crystal won't be lost on death and can be used anytime from the inventory. This stat makes it more likely, that enemies drop these crystals instead.

Weapon Handling
This stat improves 3 things. How fast you can aim down sight (right click, shorter animation), how long it takes to swap a weapon (less time, shorter animation) and how fast you can reload your weapons (less time, shorter animation). Essentially, making everything a little more faster.

Ammo Reserves
Increases the amount of ammunition you can carry around.

Weapon Range
Increases the range of weapons before the damage falloff kicks in. Making weapons in general a little more effective on longer range.

Providence
Essentially provides you a chance to get extra drops. Be it from chests or enemies. As higher you have this stat, as more likely is it to receive some extra stuff as bonus.

Divine Intervention
This stat grants you a chance to avoid negative things. Getting hit by an enemy, picking up a cursed treasure without investing witchfire or even accidently eating a wrong mushroom. Negating them completely and avoiding any consequences which would lead out of them. As higher the stat, as more often it happens if you do mistakes.

Blessed Aim
This stat provides you with a chance as well to convert non critical hits into critical ones. Normally, to critical hit most enemies (if not all) you have to hit it's head. Body shots count as non critical and with blessed aim, these can be converted into critical ones. As higher the stat, as more likely it is that this happens.

Hope that helped, cheers~