There are several different types of things you will find on the map in Harry Potter: Wizards Unite. The main things you are looking for are Traces, Foundables and Confoundables.
Traces show up on the map to help you know that a Foundable or Confoundable is near. Tap a trace to reveal a Foundable surrounded by Confoundables.
Foundables are objects, people and memories that disappeared from the Wizarding world. You need to find them to bring them back , but first you need to remove Confoundables. When you bring one back you get a sticker in your Registry. Some Foundables are whole and you only need to find them once, while others are fragmented and you need to find them multiple times.
Confoundables are magical barriers that prevent you from getting to the Foundable. They appear as webs and vines or creatures. You'll need to cast the right spells to free the Foundable.