Delayed sweep means 'after each trigger event, wait a while, then sweep the display'. After each sweep, the scope starts looking for a new trigger event straight away. This mode is useful if you have a trigger which occurs some time before the part of the signal you want to examine.
Hold-off means 'after each trigger event, sweep the display, but wait a while before looking for the next trigger event'. This mode is useful if you have a signal which contains bursts of activity separated by periods of inactivity. If you set the hold-off to be a value which is longer than the duration of the burst but shorter than the gap, then you'll get a stable display.
Hold-off achieves this by ensuring you always trigger on the first event in the burst, after all but the very first trigger. The first trigger could happen on any event within the burst, but it's guaranteed not to trigger again until after the burst has finished. The trigger circuit re-arms at some point in time during the quiet interval, and so the next trigger is guaranteed to be the first event in the next burst.