The Competitive Analysis table is intended to provide more granular look at the competitiveness of the keyword. If the Ranking Probability score answers the question "Can I rank for this keyword?", then the competitive analysis table might be thought of as answering the question "Why can I (or can't I) rank for this keyword?"
The table scores your URL, and several competing URLs, according to the 6 most important Ranking Factors: Page Relevancy, Website Relevancy, Page External Relevancy, Website External Relevancy, Page Strength, and Website Strength.
High scores are colored red, and indicate that a page scores very well on that factor. Low scores are green, and indicate that a page is weak on that factor. So what you're hoping to see is many red scores for your URL, and many green scores for the competition.
Let's look at a few examples...
Example #1: www.mangolandia.org competing for "SEO Blog"
Ranking Probability: 48% (no chance of ranking)
Lots of red for the competitors and lots of green for Mangolandia shows at a glance that this keyword is too difficult. All of the competitors score higher in all of the Ranking Factors, with particularly strong scores in the very important Page Strength and Website Strength categories. Sorry Mangolandia!
Example #2: www.rei.com/learn/expert-advice/rock-shoes.html competing for "best crack climbing shoes"
Ranking Probability: 100% (ranking likely with little or no work)
This is an example of a URL that should have an easy time ranking for the given keyword. The Competitive Analysis table shows a number of green scores, particularly in Page Strength and Page External Relevancy. In contrast, the URL being analyzed (REI) has a much higher Website Strength, and second-highest Page Strength and Page External Relevancy. Pretty much all REI would have to do is include the phrase "best crack climbing shoes" once or twice on their page and they are likely to rocket up to the #1 position.
Example #3: www.freelancetravelwriter.com competing for "travel writing"
Ranking Probability: 85% (ranking possible with work)
This chart is more complex to evaluate, and is a good example of a URL that is competitive but not dominant. We can see that different URLs rank for different reasons. For example, the Amazon URL at the bottom of the table is not considered relevant by other people (low Page External Relevancy score), but it still ranks thanks to incredibly strong Website Strength. The number 1 result has strong Website Strength, Page Strength, and Page External Relevancy, and therefore ranks #1 despite not being particularly relevant to the query. FreelanceTravelWriter.com scores well in some categories like Page External Relevancy and Website External Relevancy, but needs to improve its Website Strength if it wants to compete.