Fraudsters can use your information for many different things, such as opening financial accounts, applying for credit or committing other illegal activities.
If they don't have enough information on you to create a full identity, they can use what they already have to then access further details in scams. Common scams include phishing and vishing.
The more information a fraudster can access about someone, the more attractive that person is to them.
These methods are known as social engineering and their use is on the rise, as it's becoming easier than ever for individuals to give out their personal information.