A guarantor can be any party, including an individual or another organization, with a credit history.
If a small corporation or limited liability company lacks a credit history, and it wants the entity to be able to borrow funds, the managers and/or stockholders personally guarantee to be liable for the debt in case the organization fails to pay the debt.
[1][2] That is common in the case of corporate credit cards issued to small organizational borrowers in which the person issued the card also accepts personal responsibility for the debt as well as the corporation, so the issuer can go after either party if the debt is not paid.
In the case of individuals parents will sometimes provide guarantees for their adult children who lack a credit history.
A personal guarantee means that even if the debtor declares bankruptcy and is discharged from responsibility for the debt, the guarantor is still liable for it.