Guaranteed business loans are backed up, or guaranteed, by the SBA, which stands for Small Business Administration, or usually some other government or non-profit group. Loans that are backed up in this way give your lender the assurance that in case you default on the loan they will be paid back the majority of the loan value (the exact amount that gets guaranteed depends on your credit score and other factors). This gives lenders much greater incentive to extend funding to borrowers than otherwise.
The SBA is probably the organization that is most identified by its guaranteed business loans. They have several requirements ahead of time that determine whether or not you can receive funding. Applicants need to have a credit score over 620, must never have defaulted on government-backed loans in the past, and they need to have been in their present business for at least a year. (The last requirement can sometimes be overlooked if the applicant has had significant prior experience in their field of business.) SBA loans on average also have lower interest rates than other kinds of loans.
The SBA itself does not issue any funding, so companies that receive guaranteed business loans must take the responsibility of finding a lender willing to extend them financing. The process is much easier if you have prepared your business ahead of time, drawn up a business plan, and prepared your financial and competitive analyses, conducted market research, and can show how your company is going to succeed in its market.