A private investigator is usually a self-employed detective. Also known as PI's, private investigators are not employed by a government agency.
Because they don't work on behalf of the police, they need their own office.

They need to be extra careful on their job, as no official authority ( police, investigation agencies..) vouch for them.
If they infringe the law, like if they try to penetrate on somebody's house, if they wiretap phone conversations of if they use force to make someone speak, they may face criminal charges.

PI's are often employed to gather data on people. These data, the fruit of their investigations, may be used in a court as an evidence to charge someone.
Sometimes, they may be asked to investigate on private matters, which are beyond the scope of the law.

Their job covers the investigations of a whole range of cases: companies who suspect one of their employee to have a doubtful behavior, may appeal to PI's to investigate on him.
Many insurance companies for instance ask PI's to check the background of clients that they suspect of fraud.
PI's are also often hired on divorce cases: usually they must find evidence of adultery, as it constitutes grounds for a divorce.
Victims of a crime, of families of victims, who are not satisfied by the work of the police, or whose case has been filed in the cold case, may appeal to PI's, hoping that investigations will take a turning point.

Some countries make it illegal to practice such a professional activity, as PI's are often suspected of obstructing the work of the police. In other countries, they must be licensed, so that the evidences they collected may be taken seriously in a court.
Most of the time, their job is to tag and to interrogate people.