This amount of consumption is said to be 'autonomous' of income. The reason for this is because some minimum level of consumption is required to sustain life, so even if national income were zero there would need to be borrowing and/or international aid for the economy to continue in existence. Notice that the consumption function is always higher than zero. Similarly, if national income were higher than Y, there would be unsold goods and services in the economy, which would cause output to fall until it settles at an income level of Y. Remember that this is a Keynesian economic model, which assumes that there is spare capacity in the economy that allows output to increase without any impact on the price level. If national income were lower than Y, there would be unsatisfied demand in the economy (because the function line is higher than the AD=Y line at income levels below Y) meaning that output expenditures would be driven up in order to satisfy that demand. Starting with consumption function 1, the economy will achieve a stable short-run equilibrium point at an income level of Y, as shown. Let's start with the AD=Y line, this line shows all the points at which the economy can be in a stable equilibrium, but the actual equilibrium is determined at the intersection of the consumption function and the AD=Y line.
The graph illustrates how an increase in aggregate demand leads to an increase in national income (or national output if you prefer).