From Destinypedia, the Destiny wiki
Infusion is a feature introduced with The Taken King and boosts the Attack or Defense rating of a favored Weapon or Armor piece, similarly to the use of Etheric Light. Infusing a stronger Light-leveled piece of gear into another less powerful one will have the level increased to that of Infused piece, but will not receive any of the perks, allowing for players to choose armor or weapons for aesthetic reasons and still have good "rolls", or perks they like or want.
In Destiny 2, every Legendary and Exotic gear can be Infused with a bit of Glimmer and Legendary Shards. 4 Shards are needed if a Rare item is being Infused into a Legendary or Exotic, while only 1 Shard is required if a Legendary is used for the Infusion.