Overhangs are one of the main design challenges you will face when designing for 3D printing. An overhang is any part of your model which is not supported by anything underneath it. Since 3D printers build each layer on top of the last, any feature printed over open air will tend to droop or fail completely.
Overhangs can take many forms depending on the specific geometry of your design. While most of the time it is better to avoid an overhang, there are multiple ways to successfully print an overhang feature. Keep in mind though that these methods won't 100% fix the print and may result in unwanted side effects, if minor.
Supports are the easiest to implement because you don't have to change your design. The slicer that prepares your model for printing will automatically insert supports in the right places, and some slicers will let you manually place supports. Basically, a support is a column that is printed underneath the overhang to hold it up. It is printed with a larger than usual gap between it's top and the underside of the overhang, which means it snaps off easily without taking parts of the print with it. Multiple supports can be arranged closely to support large overhang areas.
One downside with supports is that when removed, they can leave marks on your print that have to be cut, chiseled, or sanded down. Also, you have to be able to remove the overhang and get it out/off of your print, meaning internal supports or supports blocked by complicated geometry can't be removed. This issue can actually be avoided by using a soluble support like HIPS or PVA which can be dissolved away by limonene or water respectively and leave your model intact. Another potential downside with supports is that they can add a lot of material if a big area needs to be supported. This can add to cost and print time.
A feature with nothing underneath and supported on one side is an overhang. A feature with nothing underneath but supported on 2 opposite sides or all around is called a bridge. Bridges are great because they can be printed a lot more reliably than an overhang, and often don't require supports to print nicely. This is because the extruder head can string a line of plastic from one side and firmly attach it to the other side. A print fan cools the molten plastic quickly and keeps it from drooping too much in the middle.
Bridges can be quite long depending on the printer and especially depending on how much cool air is hitting the print. Try to make your overhangs into bridges as much as possible; not only will it print better, but the resulting print will most likely be stronger too. Bridges have to be completely horizontal, not on a slant or angle, or the individual layers will not extend between both sides.
Draft is a term used in the casting/moulding/forging industries to refer to the angle given to the sides of a part perpendicular to the parting line and parallel to the pull direction of a cast/mould/forge cavity. There it makes it easier to pull the part out of the cavity; if the sides were straight friction would hold the part in. With 3D printing, a draft is an easily printable feature consisting simply of an angled wall. This can support ledges without a tricky overhang. If you can incorporate a draft instead of an overhang, your model will be easier to print, and in many cases will be stronger, too.