"Egg-bound" : when a mantis female either cannot or will not lay an ootheca and is long overdue. The female in the upper image is healthily pregnant. The female in the lower image is overdue by a month. Notice how you can see the abdominal tissue between the segments. This sort of stretching is normal when a mantis overeats, or has a large meal while pregnant, but in an egg-bound female these segments will be chronically stretched. It is important to not feed these females too much at once in order to not rupture their already-large abdomens. Female mantises can and will die from being egg-bound for too long.
While this condition can be caused by circumstances that cannot be easily resolved by their keeper (interior blockage, etc.), many times the female is simply not laying because she has not been exposed to conditions that properly stimulate laying behavior. The first steps to encourage laying behavior are typically to temporarily increase temperature and humidity, and ensure she is hydrated (using a dropper if necessary). If this has not produced laying or pre-laying (hanging upside-down, etc.) behavior within 24 hours, rearrange the female's enclosure by moving items, changing out the substrate for completely different substrate (potting soil or moss works well for this), and adding new sticks. Some females are picky about sticks being as flat and horizontal as possible, and craft popsicle-style sticks work well for this purpose. Furthermore, some females will be more encouraged to lay if more privacy is added. If 24 hours pass again with no change, try moving the female's enclosure to different areas of your domicile to give her different visual stimuli. Another strategy that has worked for several keepers is to pull up a clump of grass (including roots and attached soil) from outdoors and place it in the female's enclosure.
The egg-bound female pictured here did lay a few days after that picture was taken, once these changes were made. The resulting pictured ooth was appropriately double in size compared to an average one for this species (Creobroter aka Jeweled Flower Mantis).
