A management company is a business entity set up to manage the operations of your venture capital business. Among other things, the management company typically receives management fees from your funds, pays expenses for the overall operation of your venture capital business (e.g., hosting fees for your marketing website, travel to meet potential founders and investors), and pays the payroll of employees your venture capital business may hire.
For more information, check out our article on the AngelList Venture Education Center: https://learn.angellist.com/articles/venture-capital-management-company