It is recorded in a legalese lease exhibit that an individual pledges and guarantees to pay rent, and perform other financial lease obligations, should the tenant fail to do so.
A cost of doing (a small) business.
When the tenant is a business, a personal guarantee can provide the landlord with the relief of additional financial responsibility tied to the lease.
If the person guaranteeing the lease becomes insolvent or dies, the lease may be in default, or in a rare case, immediately terminate.
The business must find an individual willing and capable to pay what the business tenant has not. The guarantor is bound to the lease to some extent and maybe more important, accurately indicate or report those guarantees in any statement of a personal financial condition.
Personal guarantees can be limited to reasonable conditions, sometimes minimized and even in some cases eliminated entirely. Offsetting interests, like collateral, usually needs to be substituted.