Disbursement can have a few meanings. A disbursement is both the action or process of disbursing as
well as “that which has been disbursed; money paid out; expenditure” (OED). In short, it’s word we use
to refer to cash aid payments as well as the act of paying out financial aid. We also talk about "disbursement dates" which are the scheduled date of a disbursement. Many financial aid programs have specific dates that they are disbursed on.
We often use the word "disbursement" in lieu of the word "refund" because the common usage of "refund" and the financial aid usage of that word can be confusing. "Refund" is the word for a cash aid payment that is often used in formal financial aid contexts, such as the federal studentaid.gov website.
The reason "refund" is used is that financial aid is intended to pay off enrollment fees first, and then whatever's left over after that is 'refunded' to the student. In practice, almost all students who receive the Pell Grant also receive a fee waiver, so the vast majority of the award is 'refunded' in this way.