The purpose of patrol is almost the same as the purpose of policing in general. By patrolling, police officers contribute to most of the objectives that police are trying to achieve.
The major purpose of patrol is to promote and preserve order. Patrol can do this in a number of ways. By patrolling, officers maintain a visible police presence in an area. This presence can help to prevent crime because potential criminals do not know when or where the police might appear. By patrolling, police officers can help to solve crimes that have been committed. They might spot suspects as they walk down the street. By patrolling, police officers can come into contact with the public. They can find out what sorts of problems people have. They can find out about, and perhaps solve, disputes that have arisen. They can informally gather information about crimes that have been committed or might be committed in an area.
In short, patrol is the backbone of policing. It allows police to be out in the community. It allows them to make contact with the people they are protecting. It allows them to maintain a presence so that crime will be deterred and people will have better relations with the police department.