His or Her Worship is an honorific prefix for mayors, Justices of the Peace and magistrates in present or former Commonwealth realms. In spoken address, these officials are addressed as Your Worship or referred to as His or Her Worship. In Australia all States now use Your Honour as the form of address for magistrates (the same as has always been used for judges in higher courts).
Worship (style) Wikipedia
The term worship implies that citizens give or attribute special worth or esteem (worthship) to their first-citizen or mayor.
Mayors of cities and the original Cinque Ports (Sandwich, Hythe, Dover, Romney and Hastings), are styled The Right Worshipful. Also some historic boroughs, such as Shrewsbury and Atcham in Shropshire, address their mayors by this prefix. In India especially in Tamil Nadu the Mayor of Chennai is addressed as Worshipful Mayor with robes and attire as for the Lord Mayor of the City of London. The style is also traditionally used for the Vice-Chancellor of the University of Cambridge. In Australia, the Lord Mayors of Darwin, Northern Territory; Parramatta, New South Wales; Newcastle, New South Wales; and Wollongong, New South Wales are also styled thus.