A fund manager's notice to fund investors, also known as a drawdown, is a formal notice from a private investment fund (e.g. a private equity fund or venture capital fund) to its investors (usually referred to as limited partners) asking them to transfer a portion of the capital they have invested in the fund.
When an investor agrees to invest in a fund, they commit to providing a certain amount of capital to the fund. However, the fund manager does not normally require the entire capital upfront. Instead, the capital is drawn down or "called up" as needed for investments and expenses.