The core musculature is designed to resist rotation and flexing of the trunk, the plank is a great way to test and train these local stabilizers.
The plank is one of my favorites because it is easy for clients to learn, when done correctly is very safe for the spine, there are so many variations to continually challenge yourself, and there is no equipment needed so you can do it anywhere.
The key to a proper plank is to make sure you maintain a flat back. An easy way to make sure you are planking correctly is to place a dowel on your back making sure the back of your head, upper back, and gluteus are all in contact with the dowel. A great cue is to try and draw your belly button to the ceiling and squeeze the butt. Hold the plank for 30 seconds and when this starts to become easy you can challenge yourself with different variations.