The week before the August bank holiday - it finishes on the the Friday before the bank holiday Monday.

Whitby has both a free-but-on-the programme fringe, and an unofficial-for-those-who-know fringe. The season tickets for the full week are excellent value if you want to go to several of the concerts, workshops, dances and ceilidhs - it gives flexibility to try a bit then go somewhere else, but you can also pay-as-you go. £5 for a workshop I think.
If you buy a week season ticket there is cheap camping available organised by the festival, also a campsite for those attending part of the festival or fringe, run by Moor & Coast. A bit dearer but good value. Both on school playing fields.