In the most basic of terms, Schematics are Weapon Recipes and Trap Recipes that players need when using the Materials they've gained to Craft new Weapons and items. Schematics can be found in various Loot Llamas and as Rewards during a number of Quests, and they are extremely important in regards to eventually progressing nicely through Fortnite.
Each and every schematic, believe it or not, can be leveled up by spending experience points specifically designated towards your schematics, which you will obtain from completing Missions and Quests (and even inside of Loot Llamas). Each new tier/rarity of schematics will require a different number of experience points to be leveled up, with the lower rarities of Common and Uncommon costing far less than that of Rare, Epic, and Legendary Schematics.
By leveling up schematics, you will then be able to build Weapons and items that will do more damage to your enemies. Because of this, it's always recommend to Level Up your schematics; however, try to wait to do so for those top rarities of such. At levels 5, 10, 15, 20 and 25, each and every schematic will also have power increases and modifiers.