If somebody shows you a picture of their baby, you feel obligated to say something. This commitment isn't documented anywhere, but it's just a common practice. Most presenting parents want you to say something like "Oh, they're so cute" or something like that.

Having said that, let's take a look at a possible situation: a parent shows you a picture of their baby, and the baby appears to have been beaten with an ugly stick (or possibly in the looks category the apple didn't fall far from the ugly tree standing in front of you). Now, you don't really want to lie to their face, but you still feel like you need to say something.

This brings me to the word 'Precious'. Rarely is a baby actually precious. Sure, if the kid is sleeping in some supposedly adorable pose, they might merit a precious. Sometimes they can conjure up one of those innocent-like-an-angel looks and that might be precious. But for the most part, babies don't look precious.
The pause in description really gives it away. You see the picture of the baby, you say to yourself in your head "Holy Crap! That's an ugly kid!" (which is inevitably a pause), then you realize that you can't say that to the person, so you scramble for a word that would still be complimentary, but not what you REALLY want to say, so you push out the word 'precious'. That's total crap. Let's just call it how it is.

Alternate descriptions to use for a 'precious' baby

• Fugly
• Room for improvement
• Elephant Man
• Prime candidate for plastic surgery
• Unsightly
• Probably best kept in a closet
• Quasimodo
• A Shame
• Precious