Gartner Reports: How Do Magic Quadrants Work?

I feel like some folks may need to have an understanding of the Gartner 'Magic Quadrants'.  So, Im posting from Gartner's site the definitions of each section.
I got this from the following site: http://www.gartner.com/technology/research/methodologies/research_mq.jsp

Magic Quadrants provide a graphical competitive positioning of four types of technology providers, where market growth is high and provider differentiation is distinct:

Leaders execute well against their current vision and are well positioned for tomorrow.

Visionaries understand where the market is going or have a vision for changing market rules, but do not yet execute well.

Niche Players focus successfully on a small segment, or are unfocused and do not out-innovate or outperform others.

Challengers execute well today or may dominate a large segment, but do not demonstrate an understanding of market direction.