What is a Principal Disbursement?

This could be several things and your question does not state what area of the law you are asking about, but in the most common type of principle disbursement would likely be in the context of a trust, where the trust's "corpus" (think of that as the principle) can be distributed and not just the interest earned from the corpus.

In a HELOC (home equity line of credit), you borrow an amount of money (the "principal") but do not usually take it all in a lump sum. Instead, you usually receive a check book from which you can "draw" against the principal. It's kind of like a credit card secured by your house in the event you default.