Here's a good description: "A company's controller is the chief accounting officer and heads the accounting department. The controller is responsible for the company's financial statements, general ledger, cost accounting, payroll, accounts payable, accounts receivable, budgeting, tax compliance, and various special analyses."
If a company is large enough that it needs to divide up the accounting duties and responsibilities among different levels of management, then a controller would perform more complex tasks, like financial statement preparation, budgeting, taxes, etc., and hire an accounting manager or senior accountant to perform the other tasks like accounts payable and receivable, and bank reconciliations.