What is 1 damage point means in League of Legend?

What is 1 damage point means - does it mean when auto attack, 1 damage will take 1 health from opponents?

does it mean when auto attack, 1 damage will take 1 health from opponents?

On paper yes, that's it. Now, they're is one major parameter to look after when you're ingame :

Opponent's armor. Armor reduces the physical damages you will take. Physical damages come from :

• Auto Attacks (1 total AD = 1HP before armor reduction)
• Physical spells. You know the type of damages a spell deals by reading it.

Spells damages are based on ratios of either :

• Your Base AD. (what you see on your screenshot)
• Your Bonus AD. (comes from your runes/masteries/items)
• Your Total AD. (Base AD + Bonus AD)

To use Oak's exemple : Let's say you're playing zed and you're lvl 6 : You have 54.712 (+3.4 x6) = 78.712 Base AD. You have 100 bonus AD from your runes+masteries+items = 178.712 Total AD.

Now let's say you hit your opponent with 1 auto attack + 1 E (which is level 1). We will give this opponent 50 total armor and say you have 0 and 0% armor penetration.

Your auto will deal : 178.712 - ((100 / (100+178.712)) * 178.712) = 114.592 dmgs (that's the HPs your opponent will loose)

And your E will deal : 65 + (100*0.8) = 145 dmgs.

you can also reduce your opponent armor with armor reduction items. I hope this helped you, you can find every formula and every champ stats on the league of legend wiki.

Your question is somewhat badly phrased, because there are 4 types of Damage (Physical, Magical, True and Pure). There are also two stats that heavily influence damage (Attack Damage and Ability Power).

You seem to be referring to the latter: Attack Damage. Attack Damage, or AD for short, is a value that determines the strenght of your basic attacks (all Champions have AD). 1 AD = 1 Physical Damage (Before armor).

Furthermore some Champions also have abilities that scale with AD. What this means is that some Champions get more damage on some abilities, depending on how much AD you have. For example, Zed's Shadow Slash:

Zed and his shadows slash, dealing 65/90/115/140/165 (+80% bonus Attack Damage)

This means that at max level Zed's E (Shadow Slash), assuming you have 100 Attack Damage will do:

165 + AD*0.8 <=> 165 + 80 = 245 Physical Damage

In other words, and to be more specific towards your description, 1 AD = 1 damage the target will take from basic attacks, but it also increases some ability's damage. All of this is before armour reduces the damage taken.