Minecraft wiki entry for Invisibility, associated text: Mobs do not attack or sense the player until the player is a lot closer than normal.
A player with no armor can be detected at 7% of the usual detection distance.
Any single piece of armor increases this to 17.5% of the usual distance, and each additional piece increases this by another 17.5%. Full armor thus results in a 70% detection range.
After detecting the player, a mob continues to follow as if the player is visible.
Cats behave as though the entity affected is visible.
Additional methods of reducing detection by mobs include:
Sneaking reduces the detection range to 80% of usual, and stacks with Invisibility.
Wearing the corresponding mob head reduces the detection range of skeletons, zombies, and creepers to 50% of usual, and stacks with Invisibility.
Players in Spectator mode see invisible entities as translucent instead.
Invisibility prevents players from getting the Dolphin's Grace effect naturally.
Endermen have a reduced provocation range if the player looking at them is invisible.
In multiplayer and in third-person view, an invisible player's name and model become invisible, although their armor and held items do not.
Attacking any hostile or neutral mob while under the invisibility effect causes it to attack the player as though the player is not under the invisibility effect. Pillagers point their crossbows and look at invisible players instead of shooting them.
Invisibility also prevents the rendering of entity hitboxes‌[JE only] by pressing F3 + B.