The phrase "dress appropriately" is easy to grasp if you think of it this way: if you dress for your interview in the clothing you will wear on the job, then you are under-dressed for the interview. If you dress one level up from what you would wear if you work for them, you are dressed appropriately.
For example, for a man, if the normal workday clothing is jeans and work boots (as in construction or trades), or just casual clothing (as in a shopping mall retail store) then one level up is a dress shirt and complementary tie, and chinos or Dockers slacks.
If the workday rule is business casual (as in most office work) then one level up is a suit.
The only exception to "one level up" is if the workday attire is a suit (as in more formal office environments). In this case you just need to wear a suit—not a tuxedo!—for your interview.
Guys, make sure your hair and facial hair is trimmed, your shoes are polished, and do not wear any cologne, after-shave, or scented hair-gel. Many people are very sensitive to various scents, and what you think smells wonderful could make your interviewer nauseous. You don't want to be turned out of the interview right after you walk in.
If you are a woman applying for a professional or management position, wear a neutral- or darker-color suit and high heels. If you are applying for a retail or any customer-facing position you have an almost infinite number of options from dresses to pant suits, and from high-heels to low-heels. Make sure your shoes are polished, and please do not wear any perfume! None! Not even a smidgen! Remember your make-up may have a perfumed scent in it.
Ladies, the quickest path to not even finishing the interview, much less getting a job offer, is to wear clothing that is too tight, too short, too revealing, or just too provocative. In other words, "too anything." If you have any question about whether an item is "too anything," then it probably is.
Body Ornamentation
Body adornment is common today in the under-30 age group, but most office or retail environments are focused on their clients and customers, not on your epidermal artwork. Unless you are applying for a job in a tattoo parlor, or as a bouncer in a Rave club, cover all of your tattoos with clothing or concealment-grade makeup. Remove all piercing jewelry. Women can still wear pierced ear rings, but both men and women should remove every other visible piercing.