The Sharpness enchantment makes your weapon do more damage to mobs (including other players).
Sharpness is one of the enchantments in Minecraft. Each enchantment has a different purpose. In this case, Sharpness decreases the amount of time required to mine a specific block. You can mine compatible blocks at a faster rates.
Sharpness is an enchantment applied to swords. It increases the amount of damage done by a sword, and with a diamond sword at sharpness V it can pretty much kill an unarmored player in one hit.
Impossible to get
According to the wiki, Sharpness can give 1,5 hearths more damage per level. A regular iron sword does 3 damage. Sharpness II gives 1,5 * 2 = 3 hearths extra damage.
Unfortunately on non-modded Minecraft version 1.5.2 the highest level enchantment sharpness can go is IV or 4. However if you have access to a Bukkit Minecraft server then you should be able to download and add "Tim the Enchanter" plugin where you can add enchantments of any kind to any item to 127 levels.
The number for an Enchantment Table on Minecraft is 116.
The highest enchantment level in Vanilla Minecraft is level 30 through the use of bookshelves surrounding an enchantment table.
The Depth Stider enchantment increases your movement speed when you are underwater.
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Knockback is an enchantment applied to sword which knocks your opponent back when you strike it. The stronger the enchantment, the further it will be knocked back.
If you mean the enchantment then it makes the sword do more damage for all mobs. Can be really useful in the end.
Fortune enchantment in Minecraft means that the drop rate of items is multiplied. This includes items dropped from blocks including coal, diamonds, glowstones, and redstones.