There are three explanations for a downward aggregate demand curve.
The first one is the wealth effect. As many of the assets in the economy are denominated in nominal values, the higher the price level, the lower the purchasing power of money. This reduces the wealth of the economy in real terms. As a result, households and firms reduce their purchases of all goods and services and the real output drops.
The second one is the interest rate effect. As the price level rises, households and firms demand more money to finance their transactions. Given the fixed supply of money, the interest rate would rise. An increase in interest rate would cause decline in investment and consumption and also the real output.
The third one is the net exports effect. As the domestic price level rises, foreign-made goods become relatively cheaper so the quantity demanded of import increases. However, the rise in the domestic price level also means that domestic-made goods are relatively more expensive to foreign buyers so the quantity demanded of exports decreases. When the volumes of exports decrease and of imports increase, net exports will decrease. Because net exports are a component of real GDP, the demand for real GDP declines as net exports decline.