Unrelenting is an adjective that describes someone or something that is not willing to give up, like a person who tries fifty different types of ice cream in pursuit of the perfect flavor.
The word unrelenting usually describes a person who is stubborn and persistent in his efforts. An unrelenting person may also be unforgiving, such as a judge who will give the harshest sentence regardless of the sob story that the person on trial tells her. Unrelenting can also refer to non-human actions, like the unrelenting wind that finally led to a cancellation of your outdoor sailing competition or the unrelenting noise of the party that kept you awake all night.