Aspect Ratio

The aspect ratio of a photo is the ratio of its width to its height. Most system cameras and a good number of mirrorless models create photos that are 3:2 (so that there are 50% more pixels along the long edge than the shorter edge). This matches the shape of 35mm film, which is a slightly long rectangle. Micro Four Thirds cameras are the exception to the rule when it comes to system cameras, and have an aspect ratio of 4:3, which is a slightly squarer rectangle. (Compact cameras and camera phones often have a similar aspect ratio too.)

However, just because the sensor in your camera is a particular shape does not mean you have to shoot images exclusively this way. Select JPEG and you can also choose other image aspect ratios too, typically either 16:9, 4:3 (or 3:2 on a Micro Four Thirds camera), 4:5, or 1:1. (Some cameras will allow you to change aspect ratio when shooting Raw, but not all.) 

A 3:2 image like this can be cropped in a number of different ways. The 16:9 aspect ratio (the area inside the yellow lines) matches the standard aspect ratio used for digital HD television, which means any photo shot in this aspect ratio will fit perfectly when display on a modern TV. 
4:3 (the area inside the green lines) is the shape of an older analogue television, and of images shot on the Micro Four Thirds camera system.
An aspect ratio of 1:1 (the area inside the white lines) creates a square image (similar to some medium format film cameras, notably Hasselblad). Pleasing square images are strangely tricky to compose, though they are a popular shape on Instagram and camera phone apps such as Hipstamatic.

Should you select a different aspect ratio? Again, the choice is yours and you should do so if it will make a stronger, more pleasing shot. The downside to selecting a different aspect ratio is that there is no going back. There is a good argument to be made for shooting at the native aspect ratio of your camera and then cropping in post-production. If you do not like the new shape at least you can undo it at that point.