There is only one fund field that exports in the standard gift history export or the gift acknowledgment export and that is the Fund Comment field.
This field is found on the Fund 2 tab for the fund and is the first radio button labeled "Comments".
In the export, the column is labeled FundComment1, FundComment2,FundComment3,FundComment4,FundComment5 for each of the 5 possible funds you can have with a gift.
Typically information about the current projects or the focus of the granting activities of that fund are entered in this field. This field is then included in the gift acknowledgment letter to inform the donor the type of activity their gift might be supporting.