The higher your level, the higher the required souls. The number of required souls increases each time you level up.
This is the number of souls you must offer to the Fire Keeper upgrade an attribute by one point. Upon death, you will lose these souls, but you may attempt to recollect them from the place in which you perished. Souls have many purposes, most notably in leveling up your character and purchasing supplies from vendors. You must actively use them to add to this number. This does not include any souls you may have in your inventory. In a way, your current level can be viewed as a ticker for how many points you've assigned to your various attributes. Instead, you offer souls to the Fire Keeper to upgrade your attributes.
Unlike a typical role-playing game, you don't automatically level up in Dark Souls 3. Be sure to read our Dark Souls 3 covenants guide to learn about every covenant, your options and the rewards you can earn by pledging your allegiance.