Pebbles are ammunition for the slings that are used by Hobbit shirriff. You can craft pebbles by putting a block of gravel on a normal crafting table or the 2x2 crafting grid, yielding four pebbles as shown below.
vanilla crafting recipe

Pebbles deal 1-2 damage, which is less damage than arrows or crossbow bolts, but they can be fired more quickly due to the fact that they are fired from a sling in a similar way to how a player throws eggs or snowballs. This does, however, come at the cost of its accuracy. Overall they are pretty much useless as an attack unless the mob or player has no armour!

As of Public Beta 27, pebbles can be thrown by themselves, and even skipped across water!

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NPCs: Hobbit (Farmhand, Shirriff)
Traders: BartenderFarmerOrcharderShirriff Chief
Items: Leather HatMarriage RingPebblePipeSling
Blocks: Crafting TableOven
Structures: FarmHoleHousePicnic BenchTavernWindmill

Crossbow BoltAmmunitionArrow

ArrowsCrossbow BoltsDartsPebbles