Here are some definitions that will help navigating this post. There are three planes of motion that our body moves in: sagittal, frontal and transverse. Frontal is side to side movement, transverse is any type of rotating movement and sagittal is forward and back movements. Here is a picture which should help a little more.
Now that you have a little schema on the subject I will let you know why you would want to train in these planes and not just in the traditional saggital plane.
Most every activity occurs in all three planes of motion: sagittal, frontal and transverse. Even though some movements are dominating in one of the planes of motion the others are still needed. Say you dropped something on the floor and you pick it up; let us say that you choose to pick it up in this manner.

The only reason that I can think of is lack of exposure and/or relevant information. Which is the reason for this post, and even if people know about the different planes, they might not understand the importance of training in them. Two main reasons that I can think of are; to prevent injury, and to improve performance/ active life style.
Weather you are trying to stay healthy for sports or to do some gardening, you need to prevent injury to continue to do what you enjoy. Training in different planes will allow your muscles to gain; strength, endurance, and be recruited when they are needed. When doing a movement we would hope that all muscles that can help will, which is not always the case. When that happens injury is sure to follow. View the clip bellow to see a great multi-planar exercise.
Once your body is able to move in the different plans of motion it can actually produce force and give you higher performance. Now who does not want more muscles doing their job. So look up more ways to train in different planes of motion and you will prevent injury and perform better.