Asset Management is a team within a financial firm that is dedicated to managing the assets (cash, investments etc.) of clients. The asset management firm has dedicated portfolio managers as well as access to internal, detailed equity research reports which should give it an edge over investors controlling their own money.
The Asset Management service is usually offered to high net-worth individuals, sovereign wealth funds, pensions and corporations. The firm will typically charge a management fee (a fixed percentage of total funds managed) and sometimes take a percentage of the profits although this blurs the line between an asset management fund and a hedge fund.