Standing on one leg is a tricky task for young children and it takes several years before they are able to stand on one foot keeping the trunk erects with the arms by the side. 

Learning to stand on one leg without hand support starts as soon as the child learns to walk independently.

As the child learns to step up up and down, step over an obstacles or a gap, the ability to take weight and balance on one leg improves.
Children become interested in balancing on one leg from about 3 years. When they first start to practice standing on one leg they usually tip the trunk sideways and move the arms around. 

Over time and with more practice children learn to bring the trunk erect, keep the head and arms steady.  They learn to make small sideways movements of the feet to balance. 

It is only between the age of 5 and 6 years that children are able to stand on one leg with the trunk erect and steady for 10-20 seconds. 

To do this the child needs to tilt the pelvis and shift the body sideways which requires some adduction and extension of the hip. 

Children who have tightness in the hip muscles may find standing erect difficult because they are not able to effectively adduct and extend the hip.

Cadenas-Sanchez, C., Martinez-Tellez, B., Sanchez-Delgado, G., Mora-Gonzalez, J., Castro-Piñero, J., Löf, M., Ruiz, J. R., & Ortega, F. B. (2016). Assessing physical fitness in preschool children: Feasibility, reliability and practical recommendations for the PREFIT battery. Journal of science and medicine in sport, 19(11), 910–915. https://doi.org/10.1016/j.jsams.2016.02.003