As high as mountains climb as deep as oceans dive meaning

That's just another way of saying unbounded. Without limits. What can be as high as a mountain top? Nothing really, you cannot climb higher than a mountain peak. And what can be deeper than the ocean depth? Similarly, you can't dive deeper than the ocean depth. When we talk about mountain peak say of Everest. or ocean depth like say the Mariana's trench; our intellect cannot conceive any parts of the habitable world higher or lower than that. So the idiom means unbounded or without limits.