There are many reasons for you to use warrant search facility. One important reason is that you may have a police warrant issued on you for not paying a fine for a petty traffic offence. When you make your search, if you find that you have a warrant against you, it is quite possible that you will get reminded of the cause.
Even if you don't remember any cause, you could surrender yourself to the authorities through a lawyer and settle the matter. Even if you remember the cause you need the help of a lawyer to settle the issue once a warrant has been issued.
Another reason when the search option on warrants come in handy is when you are going to employ a house maid or a baby sitter. Since you have the facility to look at the background details of the person over the internet, you have the possibility to recruit the most suitable person for the job.