It depends on how many shareholders there are on the record date. The fund will collect dividends from the paying companies based on the number of underlying shares that it owns. On the record date, they have to pay out those dividends to all of the fund shareholders.
Let's say there's an IBM fund which invests in IBM stock and distributes IBM dividends to the fund's shareholders. On IBM's record date, the fund might own 100 shares. If IBM paid a $1 dividend, then each of the fund holders would get a $1 dividend (minus any of the fund's fees).
But, if the fund's record date come after IBM's record date and a bunch of people bought into the fund in the meantime, then the dividend would have to be equally divided among all of the fund's shareholders thus reducing the yield.