When the explorer's hat item is worn, any hostile mob that would normally attack players will instead ignore the player. When worn, peaceful mobs (the rabbit and penguin, which are currently the only peaceful mobs in the game) would not run away from the player. Agressive mobs (such as boars and hawks) calm down twice as fast.
Be aware that hostile mobs can still damage players with explorer's hat if they keep following it, accidentally touch it, or vice versa. Furthermore, mining or attacking (even if the player fails to hit anything) disables the explorer's hat effect for 10 seconds.
The explorer hat acts as a very weak chapka. In the forest at nighttime, your heat decreases by 15 every 5 seconds (as opposed to the usual 18). It does not provide any protection from blizzards.