What is a sublet?

Essentially the question has been answered by yourself. 'to lease or rent ones property to another' So essentially you can rent a place/house and then either sublet/rent a house/rooms to another, so you let the house on the original agreement with the landlord where as if you rent it out to another your subletting the property to them .

If you rent an apartment or house, then you turn around and rent it to someone else and you are not living on the premises, then you are subletting the residence. People tend to do this if they decide to travel for a year that way they have a home to come back to and an income from the sublet (someone to pay the rent). Many landlords do not allow sublets and would indicate that in the lease. When they rent out a residence they do background checks, especially financial, to ensure they will be getting their money. If you rent your rental out to someone else, the landlord will not know the person or their background, which is why they wouldn't allow sublets.

This is usually applied to apartments as living space. If you are renting a place and then let someone else rent the space from you, you are subletting the apartment.