Sometimes you may have to find someone who has, for whatever reason, made it hard to find them. It may be that they simply moved on without a forwarding address, but it also may be that they are deliberately hiding. It does not matter - hard to find is hard to find.
The reason you are searching for someone does not matter. You may want to search for a person simply to get in touch with an old friend. But you may also be searching because, for example, they owe you money or you need their help in a legal matter. Or you may be searching because you are considering hiring someone who needs to have a clean driving record.
The reasons you have their license number can vary as well. You may have their driver's license number because they had to provide you with a copy in order to, say, cash a check or sign a lease or apply for a job.
Regardless of why you have it or why you are looking for them, if you have someone's driver's license number, finding them or information about them can become much easier, although not necessarily free to do.
While searching for people when you have other details can often be as simply as typing the information into your favorite search engine, the likelihood this will work with a drivers license number is practically nonexistent.
If you are checking someone's records for employment purposes, you will need to access Registry of Motor Vehicle records. You can request someone's driving record and other related information yourself, or you can use a third-party service. You also need the permission of the person who's driving record you are requesting. You can make your request in writing or in person from any DMV office or examination station.
On the other hand, if you are trying to find someone and do not have their permission, you will likely need to use the service of a private detective or specialized third-party service as such records are not made public to just anyone without permission. There are exceptions to the permission requirement, such as for use in court proceedings, but using a third-party (be it a detective, attorney, etc.) will likely be worth the money.