Budgetary control is financial jargon for managing income and expenditure. In practice it means regularly comparing actual income or expenditure to planned income or expenditure to identify whether or not corrective action is required.
For example most University departments are given annual chest budgets for general equipment. By regularly comparing actual expenditure on this budget to planned expenditure a department will be aware of whether a particular item can be afforded. If the account is in deficit a department will need to identify an alternative source of funds (e.g. departmental reserves or charging to a research grant or contract). This process of monitoring expenditure and taking appropriate action is known as budgetary control.