Origins of the phrase
According to Collins Dictionary, to beat the bounds is “to define the boundaries of a parish by making a procession around them and hitting the ground with rods”. The origins of this go back more than 1,000 years in England. Two kinds of  beating took place: not only boundary stones or other markers were hit, but also young boys. The pain of the beating, or being bumped on a stone, was meant to burn the event into their minds, so that the course of the parish borders would remain in the communal memory for many years to come.
Why beat the bounds?

Parish boundaries mattered because they determined property rights and obligations.  It was important to stop neighbours from encroaching and to know who could be buried in the churchyard, who had to pay for church repairs and who paid taxes for feeding and housing local paupers, which was responsibility of parishes for centuries. Beating the bounds, alternatively known as “perambulating”, was often combined with processions at the church festival of Rogation in spring before Ascension Day, when the priest and parishioners prayed for a good harvest. It was also associated with drinking and riotous behaviour.
Where the tradition survives

There are survivals and revivals of the practice in many places. At Bodmin the custom was resurrected in the 1860s and involves an eighteen-mile walk followed by a game of Cornish hurling – a silver ball thrown into a pool by the mayor is carried along a fixed route. At Richmond in Yorkshire the mayor, dressed in full regalia, leads a crowd of dignitaries and citizens every seven years and wades into the River Swale where it marks the boundary. At Poole in Dorset, the border between the open sea and the harbour is established by boat. In Oxford, where the parish perimeter of St Michael at the North Gate has been obscured by building, the priest and his flock carry their willow wands into a Marks and Spencer’s store, shouting “Mark, mark!” The Liverpool Arts Lab organises a walk around the limits of Toxteth Park as a creative happening, substituting rituals of death for spring prayers for the crops. In London, St Martin-in-the-Fields allows everyone to beat its bounds virtually by means of an app, and the ancient precinct around the Tower of London is perambulated annually by Yeomen of the Guard with school children and choir boys. At the border of this precinct with the parish of All Hallows-by-the-Tower, a violent confrontation between the two sides took place in 1698, so All Hallows defends its territory with a procession. To see some entertaining footage of ceremonies held in the twentieth century, search the term on Youtube.
The tradition was carried to North America long ago and survives in New England. In Germany, too, a similar event takes place every seven years in the town of Biedenkopf, which contested the rights to a forest with a neighbouring community in 1525 and now celebrates the practice with a festival.  

The walk described on this website is a non-religious, non-violent perambulation. I have no plans to beat anybody or anything.