Every individual gets the personal allowance, that is the amount you can earn tax free. This is converted to a tax code which tells the employer how much tax to deduct.
The personal allowance is £6475 this year, which gives the code 647L. So with one job you would have that code, and you would get £6475 tax free (spread over the year) and anything over would be taxed at the appropriate rate, which would likely be 20%.
With three jobs, the code will be given to the one employment, and the other two would be taxed with the code BR, which means all of the income is taxed at the basic rate (20%).
So, if one job will bring in an income of more that the personal allowance, the other two will have the code BR, and all will be correct.
If none of the jobs are over the personal allowance then you can ask hmrc to split the allowance. For example:
Job 1 - £3000
Job 2 - £3000
Job 3 - £3000
so, total income £9000, of which £6475 can be earnt tax free. HMRC could split the allowance so that £3k goes to job 1, and £3K to job 2 and the rest, £475 goes to job 3. This would give the following codes:
Job1 - 300L
Job2 - 300L
Job3 - 47L
So, no tax would be paid on jobs 1 and 2, as there are enough allownaces to cover the income, and £2521 of job 3 would be taxed at 20%.