Wands of Preservation are found rarely in Amber clumps, preserved within the rock. In order to acquire one, you must break the block of Amber it is inside; the block will then drop the Wand of Preservation stored within.
These wands are used to, like the name says, preserve things. When combined with Amber Stars (which are used as ammunition), right-clicking with a Wand of Preservation will lob a ball of what can be assumed to be magically liquefied Amber (not Tree Sap; technically, real Amber cannot melt, and simply burns) that is affected by gravity.
If a ball connects with a non-boss mob (except for an Umbergolem Idol Guardian), the mob will despawn and be preserved within a specially textured block of Amber, called a Preserved Block. The mob will be visible inside the Preserved Block.
If a Preserved Block is broken without using a pickaxe enchanted with Silk Touch, the mob within will spawn, including all additional data associated with that mob (i.e., a Wasp spawned as a Hornet of Despair will emerge as a Hornet of Despair, and the uber-rare Ender Dragonfly will also spawn as an Ender Dragonfly).
When broken with a pickaxe enchanted with Silk Touch, the Preserved Block will drop itself with the mob still inside. Preserved Blocks are programmed to ensure that you don't accidentally spawn a mob you've caught, and as such always take ten seconds to mine, regardless of Efficiency enchantments or tool quality.
If you miss a shot with a Wand of Preservation, the liquid Amber ball will spawn an empty Preserved Block wherever it lands, including on walls and ceilings. These blocks act the same as a Preserved Block with a mob inside, with the exception of not spawning or displaying a mob.
Wands of Preservation can be repaired on an Altar of Repair.