The world of Dark Souls is a very unforgiving place, and when you first get started on your journey here, they don't exactly explain a lot of the stats to you. It is mostly up to trial and error to see what they do yourself. Below, I'll explain each of these stats for you to give you a helping hand, and lets face it, we probably all need it playing this.
Vigor
Vigor is one of, if not the most, important stat for you in Dark Souls. This is what determines your total health and no matter your play style, you are probably going to want to invest in this to avoid instant death.
Attunement
Attunement is important for casters, as it will give them more focus power and spell slots the more you invest in it. If you want to have a variety of spells at your disposal, and be able to cast them often, you'll want to invest in this.
Endurance
Endurance is what determines how much stamina you have, which determines how often you can roll to dodge, attack, how much you can block with your shield, or run. Blocking an attack with your shield essentially damages your stamina rather than your health, depending on the shield. If you don't have enough stamina to absorb it all, you'll get staggered and lose health anyway.
Vitality
Unlike other games with a vitality stat, it doesn't determine your max health, but instead how much you are able to carry. This is important if you want to build a heavily armed and armored character who can still roll quickly. It is best to keep your equipment load around 70%, anything higher and you won't roll too far. This also provides you with some poison and physical defenses.
Strength
Strength is going to be important if you are looking to use any of the heavy weapons that scale off of it, like axes, clubs, or hammers. The more strength you have, the more damage you will do with any of these weapons.
Dexterity
Much like strength, this increases the damage of different types of weapons, such as daggers, bows and light swords. If you're looking to build an archer, or just a quick attacker, this stat is for you.
Intelligence
This increases the damage of both sorcery spells, and certain intelligence based weapons like the staff. Sorcery shouldn't be confused with miracles though, increases in faith are required for those.
Faith
Much like intelligence, this will increase your spell damage for miracles, rather than sorcery, and increase damage with faith based weapons.
[/b]Luck[/b]
Last, and probably least, is going to be luck. In dark souls you are either quick or you're dead, luck isn't going to save you.It can increase your item discovery, and your bleed, poison, and curse resistances, but it really isn't worth it, invest in a better stat and rely on skill, not luck.
Hopefully this list helps. Also, something to keep in mind for the stats is that as a general rule, a stat of 40 is going to start getting diminishing returns for anything higher than 40. So while you will still benefit from increasing the stat, it is probably better to spend those stat points elsewhere instead.
Vigor
Vigor is one of, if not the most, important stat for you in Dark Souls. This is what determines your total health and no matter your play style, you are probably going to want to invest in this to avoid instant death.
Attunement
Attunement is important for casters, as it will give them more focus power and spell slots the more you invest in it. If you want to have a variety of spells at your disposal, and be able to cast them often, you'll want to invest in this.
Endurance
Endurance is what determines how much stamina you have, which determines how often you can roll to dodge, attack, how much you can block with your shield, or run. Blocking an attack with your shield essentially damages your stamina rather than your health, depending on the shield. If you don't have enough stamina to absorb it all, you'll get staggered and lose health anyway.
Vitality
Unlike other games with a vitality stat, it doesn't determine your max health, but instead how much you are able to carry. This is important if you want to build a heavily armed and armored character who can still roll quickly. It is best to keep your equipment load around 70%, anything higher and you won't roll too far. This also provides you with some poison and physical defenses.
Strength
Strength is going to be important if you are looking to use any of the heavy weapons that scale off of it, like axes, clubs, or hammers. The more strength you have, the more damage you will do with any of these weapons.

Dexterity
Much like strength, this increases the damage of different types of weapons, such as daggers, bows and light swords. If you're looking to build an archer, or just a quick attacker, this stat is for you.
Intelligence
This increases the damage of both sorcery spells, and certain intelligence based weapons like the staff. Sorcery shouldn't be confused with miracles though, increases in faith are required for those.
Faith
Much like intelligence, this will increase your spell damage for miracles, rather than sorcery, and increase damage with faith based weapons.
[/b]Luck[/b]
Last, and probably least, is going to be luck. In dark souls you are either quick or you're dead, luck isn't going to save you.It can increase your item discovery, and your bleed, poison, and curse resistances, but it really isn't worth it, invest in a better stat and rely on skill, not luck.
Hopefully this list helps. Also, something to keep in mind for the stats is that as a general rule, a stat of 40 is going to start getting diminishing returns for anything higher than 40. So while you will still benefit from increasing the stat, it is probably better to spend those stat points elsewhere instead.