Wearing a more formal outfit than you would on a day-to-day basis to a job interview, as the previous answer states, gives the sense that you care about the job. There are people out there that consider that “casual”, but that’s for a different answer.
If you care about the job and about your chances of getting it, you’ll show it through not only dressing appropriately, but by reaching on time, listening to the interviewer, etc. Especially if you’re prepared for it before the interview comes.
One other reason to wear a more formal outfit (think business dress rather than full on formal dress) is that it simply shows that you respect other person’s precious time. Someone is giving you time out of a busy day to see if you’re the right fit for the job. Show them that you respect them.
You wear formal clothes for an interview as a sign of respect. It also conveys the sense that you are serious about the job and have taken trouble to attend looking professional. If this was the job of your dreams that you have been short-listed for, would you turn up late?
No, of course not, so you wouldn't turn up scruffy, or even casual. Casual says to the interviewer that you don't care much whether you join the company or jog down to the park.