Hi,
As Perdie said, this is basic rate tax code - it's usually given if no P45 is supplied (which will be the case for your DP, as he has been out of work for over a year), or if you have a second job.
What it means is that all earnings with that tax code will be taxed at basic rate (20%).
JSA is taxable, see here but whether or not your DP actually has to pay tax on it will depend on how much he receives - it may fall under the personal allowance of £6,475, which is tax-free, and how much of it is taxable. What this means, roughly is that if he has (or will) gone over the £6,475 annual limit, all other earnings will be taxed at 20%.
Because JSA is taxable, and he will be going back onto JSA, you won't be able to reclaim any overpaid tax until the end of the tax year, as the benefits he will receive will affect any refund he may be due.
He will need to give his P45 from the temporary work to the Benefits Office in order to ensure he gets any tax refund he is entitled to.
If he is still claiming JSA at the end of the year, the Benefits Office will normally repay any overpaid tax at the end of the tax year.
If he stops claiming JSA before the end of the tax year, the Benefit Office will normally repay when he stops claiming.
There's some more information here. I would recommend giving the Tax Office a call though - it may be that they can move him onto an emergency tax code (647L), which would at least mean his Personal Allowance would be taken account of, and they may be able to advise you if it is possible to get an early repayment.
Hope that helps, although I know it's not goods news