These are quite different words, but you may see impassible as an incorrect spelling of impassable because impassable is much more commonly used than impassible.
Impassable is an adjective meaning “not able to be passed”:
The mountains were so rocky as to be impassable.
Impassible is an adjective meaning “not able to feel pain” or “not able to feel emotion.” Most often the word impassive is used instead.
Impassive means “not feeling pain or emotion” which is almost the same as impassible, although there is a slight difference. Impassive describes a person at a particular moment when they are feeling nothing, while impassible can also describe a person generally unable to feel pain:
The psychopath seemed impassible; he never showed any fear or regret.