What does withholding means on my Unemployment Insurance claim form?

Yes, mark it. Unemployment comp is taxable income. They'd take out $37 from each uc weekly check - at the end of the year you'd likely be OK, unless you get a high paying job to put you in a high bracket in which case you could still come up short if they deduct 10%. Withholding works the same for uc as for paychecks.