The total amount of money investors have trusted to a fund manager to invest across all their investment products.
The Funds Under Management (FUM) figure is typically used by fund managers to show how much money investors trust them with - the larger the figure, the more money they have invested on behalf of investors.
While Funds Under Management might indicate the maturity or level of experience of a fund manager, it does not indicate anything about past performance, nor about potential future performance - although one might argue that if a fund manager performed poorly, then their Funds Under Management would drop as investors took their money elsewhere.
Given that most fund managers earn their incomes by way of an annual fee based on the assets held in each of their funds - the Funds Under Management can also be an indicator of the profitability (or at least of the revenue) of a fund manager. A drop in FUM will generally lead to a drop in income to the fund manager - and similarly increases in FUM will generally increase revenue.
Note that Funds Under Management is not just a reflection of the amount of money trusted to the fund manager by investors, since capital growth of the assets held by the fund manager will also contribute to the growth in FUM. As such it is insufficient to look at the FUM figure alone as an indicator of how much investors trust the fund manager - and the difference in growth from contributions versus from capital growth of the assets is typically not transparent.