In general, it is the price of a swap– i.e., the amount paid by the swap buyer to the swap seller. The swap could be an interest rate swap, or a credit default swap (a default swap), etc. For an interest rate swap, it is an upfront amount paid or received in connection with the execution of a new swap or the assignment of an existing swap position.
In a credit default swap, this premium (known as CDS premium) is the premium (measured in basis points) that is paid to the protection seller in a credit default swap (CDS) or a similar credit derivative. It is what a protection seller gets paid for the credit/ default protection (that is provided to a protection buyer).
