The gutters of many homes have downspouts that connect to secondary drains which extend underground to an intended exit point elsewhere. These are also commonly called drain tiles, french drains, or downspout extensions. In every case, the goal is to take the enormous amount of water your roof and gutters collect and neatly divert it safely away from the home. In most cases these lines are 4" corrugated and/or PVC pipe, and ideally end in an elbow with an opening/closing cap.
Over time these lines fill with debris and require maintenance. The debris responsible for most issues is far and away shingle gravel – it takes a few years, but eventually enough of this sandy material builds to restrict flow and ultimately allow roots to grow through like soil. Just as commonly, the exit points or "caps" of these underground downspout drains are totally unknown. Usually this is because the cap is simply covered over by sod, but if so it's automatically overflowing. We wrote a full article on what causes these clogs if you want the details.
If your extension can be picked up or you are able to reach your arm in from either side and reach the entire length, you can absolutely do this yourself. Otherwise, this is a difficult task to do thoroughly as a homeowner. Even in an ideal situation with a known exit location and not requiring any specialized attachments (for roots, corners, etc) the amount of sediment alone requires a volume of guided water flow that even consumer pressure washers, let alone simple garden hoses, just cannot provide. You need to both break through the clog and flush away all the remnants – and do so without damaging the fairly delicate pipe walls. This requires niche equipment; we have to order most of our attachments all the way from Australia.
The good news is that this maintenance isn't needed more than once every few years (3-5 works) but it can literally save you from a nightmare flood situation. Here at Done Gutter we offer clearing and restoring these buried downspout extensions via pressure jetting to break up the contents and flush it all out. This is our bread and butter, and if you're in the greater Indianapolis area we'd love to help. If not, we hope we can get you on the right track at least with what you're looking for.
Just because you have these drains doesn't automatically mean you have an immediate problem. Not sure if your underground downspout extensions are clogged yet? Here's some signs.