Monetary policy refers to the Central Bank's action on money supply, and therefore its effect on interest rates. A tightening, therefore, refers to raised, or high interest rates, such as if the UK raised interest rates from 3% to 5% in light of a sharp rise in inflation rates.
Interest rates are defined as the cost of borrowing and the reward for saving money, and so if they are increased, it becomes more expensive to borrow money. Households and firms are incentivised to save their money instead of spending it. This decrease in spending is represented by a decreased level of consumption, and therefore we can conclude that a tightened monetary policy will most likely lead to a decrease in consumer spending.
(As I would now show in a diagram)
The decrease in consumer spending is represented by a decrease in AD (Aggregate demand), which is defined in terms of its equation: C + I + G + X - M. AD shifts to the left as a result of decreased consumption (and investment) as more consumers now cannot afford to borrow money as the higher interest rates mean that they have to pay a higher return for each pound that they borrow.