Potion of Invisibility is a consumable potion added by vanilla Minecraft.
The invisibility potion effect makes a players nameplate and skin invisible for the duration of the effect. It also makes hostile mobs neutral around that player unless the player provokes them, or is wearing armor or has an item in his or her hand (as they are not effected by the invisibility). Other players cannot see you either unless they have a trained eye (as the effect particles are also visible) or you are wearing armor or holding something in your hand. If you have multiple effects, including invisibility, the other effect particles will remain visible. If you are set on fire, the fire will be clearly visible.
If mobs are affected with this potion effect, their bodies will become invisible, but the particles the effect emits (as well as their armor and weapons) remain visible. If both the player and a mob are completely invisible, they will not be able to see each other.
The only way to gain this effect is to brew a Fermented Spider Eye with a Potion of Night Vision to create the potion, or use the Cloak of Distortion's effect which gives the player invisibility for two minutes in exchange for an Ender Pearl.