Minecraft wiki entry for Dual_wielding, associated text: Players can now use both hands to do different actions with the left and right mouse buttons.
For example, if a player has a pickaxe in their main hand and a torch in their off-hand, right-clicking will place the torch.
This happens because a pickaxe lacks a right-click use, and therefore the game tries to then treat the other item as if it's being right-clicked.
Players can put an item on the "off-hand slot" in their inventory to hold it on their off-hand.
It is distinguished by an outline of a shield like symbol.
Pressing F (by default) will switch whatever item is selected in the hotbar with the item in the off-hand (including no item).
The off-hand slot is displayed next to the HUD when it's not empty (left for right-handed players and vice versa).
Only the main hand can be used for attacking or breaking.
An exception is items which do damage upon using them, such as bows or splash potions.
Bows determine what type of arrow to shoot based on the player's inventory and off-hand.
Arrows in the off-hand take priority over arrows in any other slot.
Otherwise, the closest stack of arrows to the first slot is used.
If the bow is in the off-hand, the selected hotbar slot takes priority.
If there are multiple arrow types and none held on the off-hand or main hand, the arrow on the first hotbar slot will shoot first.
The off-hand is invisible in first person view while it's empty.