A loan origination fee is the fee that a borrower pays to a lender simply for the act of setting up the loan that is to be given to the borrower. In the context of the law, this fee is usually required by law to be paid by the borrower to the lender if the borrower takes the loan, and this fee is included with the loan.
The reason why loan origination fees are included with loans is because loans take time and effort to set up on the part of the lender. For example, if a bank is giving a mortgage loan to a borrower, the bank must pay an employee to process the loan application, check the borrower's credit, decide how much to offer the person, etc. So, originating the loan costs money for the bank. However, many borrowers are willing to pay this fee in order to get access to the loan, so that they can buy their house, pay for grad school, etc.