A double ureter means that a kidney is drained to urinary bladder by two different tubes instead of just one. Such abnormality is seen in 0.2% of live births. While one ureter drains the top of the kidney and another one drains the bottom part of the kidney. These ureters may be duplicated for the complete length till bladder, or may unite en-route (partial duplication). Some other kidney birth defects may be associated with complete ureteric duplications, like swelling of upper part (hydronephrosis) or reflux of urine into the lower part. People with double ureters are prone to get urinary tract infections. Such problems are less likely to happen with partial duplications. Partial duplications, though, may increase technical difficulties during surgical interventions as may be required for the stone, as in your case.