A lease incentive is something given to, or on behalf of, the lessee. Examples: paying off a penalty for breaking another lease (for an office space, for instance); leasehold improvements; a cash bonus or other gift. Initial Direst Cost (IDC) is money spent by the lessor or lessee to complete the transaction, such as a commission to a broker. The incentive directly benefits the lessee; a lessor's IDC doesn't.
IDC is much more tightly defined than it was under FAS 13/IAS 17, when it included other costs for leasing like contract preparation charges, marketing, and the like. Now it's limited to expenses that would not have been paid if the lease had not been completed.