Income in respect of a decedent is income a person had a right to receive at death but which was not properly includible on their final income tax return under their method of accounting. IRS Publication 559 puts it in one sentence: "All income the decedent would have received had death not occurred that wasn't properly includible on the final return ... is income in respect of a decedent." Internal Revenue Code section 691, headed "Recipients of income in respect of decedents," is the governing provision, and the Instructions for Form 1041 abbreviate the phrase to IRD.
The everyday examples are unremarkable: a final paycheck or commission unpaid at death, interest accrued on a bond but not yet credited, a consulting invoice outstanding. The consequential example is a traditional IRA or 401(k) balance, which is the largest asset in many estates and which is IRD in its entirety to the extent it was never taxed.