Babies bond through smell, so mom should avoid scented products and deodorant in the newborn period so as not to interfere.
Unlike some of the other weird advice, this is one that sounds weird and crazy, but it's actually good advice. Baby's sensory systems are brand new and adapting to a whole avalanche of new stimuli. Researchers have shown what mama knows instinctively - babies are soothed by the mere presence of her scent. And animal studies suggest that that repeated exposure is critical to bonding and brain development.
As usual, Mother Nature has helped us along in this regard: in the post-partum period, it's not uncommon for mothers to have a heightened sense of smell. I recall cursing my husband in the early weeks after my daughter was born because he would spray his cologne in the bedroom before he left - I could smell it for hours (and not in a good way).
Scented products are also likely to be hard on post-partum and newborn skin. Your bottom may feel like it needs to be refreshed, but whether you had a vaginal birth or a c-section, the, um, exit point is likely to be irritated by scented soaps and creams. And given the degree of medical intervention accompanying most births (including lots of antibiotics), a yeast infection will not need much encouragement.
Scented soaps on the breasts and nipples can make sore nipples worse by encouraging irritation. Use nothing but water on the your breasts - a little breastmilk at the end of a feeding and air drying can help with mild soreness.
With respect to deodorant/antipersperants in particular, infants are eating pretty close to the application point. And if you've read the labels on these products, they're not something you want your newborn baby licking.
Finally, a very good side effect is that without lotions and potions to hide behind, mama will be more motivated to get herself in the shower everyday. And a daily shower is reason enough to make this weird advice very smart indeed.