Kryptonians are very strong, but they aren't unbreakable. Their armor, which appears to be made of various super-dense elements is both ornamental (identifying their clan and affiliation) and functional. It prevents them from coming to physical harm, on their homeworld, where they merely possess modestly superhuman strength and on Earth, where they possess godlike abilities.
Jor-El's armor is of a very similar construction to Zod's
An avalanche of pulverized carbon and silica smashed him to the floor, burying him beneath heaps of rubble.
His armor shielded him from serious injury, but he found himself trapped, unable to move.
The armor also serves as an environment suit
She walked briskly across the runway toward Superman; confidence
echoed in her every step. She saluted him with military precision and
activated a control on her armor. Her visor went transparent,
revealing the striking feature of an attractive female with short dark
hair and icy brown eyes. Like Jor-El, she could easily have been
mistaken for human.
It's quite daunting
Clearly female, she wore an intimidating suit of jet-black armor.
Jagged fins added to the uniform’s fearsome aspect. A space helmet,
with a visor that consisted of an opaque force field, concealed her
features—even from his X-ray vision.
All quotes from the film's officially licensed novelisation by Greg Cox