Refers to a person, task, or thing that is a troublesome burden or a hindrance. Often used in the phrase 荷厄介になる (to become a burden).
He is always a burden.
This old sofa became a burden when we moved.
お荷物 is a more colloquial and slightly softer term for a person who is a burden or a hindrance, literally 'luggage'. 荷厄介 is more formal and can refer to both people and things.
Compound of 荷 (ni, 'load, burden') and 厄介 (yakkai, 'trouble, bother'). The combination emphasizes a troublesome burden.