Metzler diagram interpretation
It is because supply of saving is equal to the cost of saving which is forgone consumption as the graph notes. To explain this further the vertical distance from $x$-axis to the supply curve gives you the value of forgone consumption for some infinitesimal increase in the supply (along the supply curve). This is because value of the forgone consumption needs to be at least equal to the ‘quantity’ of output you decided to save rather than consume times the return you earn on those savings (otherwise you would not supply those savings to the market to begin with).
So the total cost of saving will be the sum of all costs of savings for every small increase in the number of saving (i.e. every difference between the point on supply curve and the $x$-axis). The sum of these adds up to the area under supply curve up to the point where actual return intersects the supply of savings.