To sublet or to sublease is to rent your apartment/house to someone during your own lease term. This second lease, a sublet lease, does not release the original tenant from the obligation to fulfill all the terms of the initial lease. Subletting is a good way of temporarily transferring the obligations of a lease, whether during summer or while away for a semester abroad.
When signing a lease, make sure that subletting is permitted by your lease. Most leases allow subletting, but they usually require additional written consent by the property owner or manager. Consent cannot be unreasonably denied. Denial of consent can only be based on financial assessment and credit history of the potential subtenant, not on any discriminatory factors.
Be aware that the original tenant is still bound to the terms of the lease, should the sublettor fail to fulfill any of the obligations of the lease. By the same token, the subtenant's obligation is to fulfill all the terms of the original lease. It makes very good practice for both the original tenant and the subtenant to read and understand the terms of the original lease. This is the surest way to avoid problems that can arise with subletting.
Whether you are the original tenant interested in subletting your apartment or the potential sublettor, keep in mind the following: