As describe by the wiki, Balut is a fertilised bird egg (usually a duck) which is incubated for a period of 14 to 21 days depending on the local culture and then boiled or steamed. The contents are eaten directly from the shell. Balut that are incubated for longer periods have well-developed embryo and the features of the duckling are recognizable. The partially-developed embryo bones are soft enough to chew and swallow as a whole.
As for eating, eat the balut directly from the shell not the shell itself. Look at the egg to see which end is larger, peel the top part of the shell, break through the membranes and sip the amniotic fluid liquid from the egg. The yolk and embryo are completely edible. The albumin too tough to eat and discard it. We Filipinos traditionally season the egg with salt, vinegar or soy sauce as we eat it. Although balut might not sound appealing if you haven't grown up with it, it does make a nutritious snack, high in protein and calcium.