"The hump" is a colloquial term, almost slightly humorous in nature for a number of reasons. In a literal sense, it refers to the highest point on a hill, the point that takes the greatest amount of exertion or effort to overcome or get past due to gravity.
When used figuratively outside the context of a hill, it is used to describe a specific point in a task, action, or condition that requires the greatest exertion or effort to accomplish, implying that everything that comes after is easier than what came before (which leads to another idiom, "all downhill from here"). It also can be described as the worst or most difficult part of a task, action, or condition.
Examples -
"Now that our friend has found an organ donor, he is over the hump and has a higher chance of recovery."
"Once we make it halfway through this marathon, we will be over the hump of this race."
Similar idioms -
"Out of the woods"
The first sentence is used in this manner. The second sentence does not make sense in American English.