If you have the tax code letter M or N after the number in your tax code notification then these two letters are linked as it means that you have either transferred or have received a transfer of the 10% personal allowance to/from your partner.
The marriage transfer allowance was introduced so that those who did not pay tax on their earnings up to the full personal allowance, could transfer 10% of their allowance to their partner (as long as their partner was only paying basic rate tax).
So, for example if your tax code for 2018/19 is 1304M that means that your partner has transferred 10% of their personal allowance to you (amounting to £1,185).
This 10% is added on to your personal allowance of £11,850, giving you a total personal allowance of £13,035 (the figures are rounded for the tax code).
Conversely, if your tax code is 1066N then that is likely to be because you have volunteered to give up 10% of your personal allowance to transfer over to your partner who can make use of it. You can do this if you don’t use all of your personal allowance.
This is worked out by taking £1,185 away from £11,850, thus giving you a personal allowance of £10,665 (figures are rounded).
(The above figures are based on amounts for the 2018/19 tax year.)
If you believe that your tax code is wrong then you should contact HMRC on 0300 200 3300.