Gutters, wow they can cause some serious trouble if not properly flowing. The goal is to transport the water away from the house.
You can see if the down spout is .not working above the ground. What about below the ground? The conductors should be above grade. They should be tested and confirmed that they are flowing to an exit point; to a storm sewer, ditch or another type of run off.
Snaking and hydro jetting these lines is obviously very important to keep the water off your foundation. You do not want foundation issues with your home, as it is an extremely expensive repair! The above photo is an example of the issues that can arise as a result of gutters not functioning correctly.