Advance pay, any payroll staff here?

Can someone explain to me how advance payments work? I have done KIT night shifts and received payslip for it but this only included the enhancements. So I disputed it with my manager and HR as my annual leave didn’t get included either so they’ve said it’ll be sorted and I will be given an advancement but not sure what this means or how this works?! Do I get taxed more in December or January pay?