Is that it in the back corner? If so, it's a drain.
The stains are due to water penetration. Back wall looks like concrete. If so, it's seepage - meaning that the yard drainage outside the wall is not quite right. If the garage opens into a lower level of the house, you can bet that the same back wall has the same kind of issue.
A good indepenedent inspector (and I stress "good") could tell you for sure, but my best guess based on pictures is above. Likewise, if you're serious about the house, have mold testing done.
Good waterproofing is neither cheap nor easy. It has to be done from the outside, which means digging up the dirt along the wall, coating the outside of the wall, putting in appropriate drain pipes, and regrading the land so the water flows away from the house. If the house is carved into a hill, water flows downward towards the wall.