Query Stats
Here you will see 2 tables:-
Top Search Queries shows you the top Google search
terms over the last 7 days that resulted in a page from your website
being returned, as well as the average position of your listing on the
page.
Top Search Query Clicks shows the top search queries over the last 7 days that resulted in visits to your site.

This tool can be used to spot any pages that may well be showing up in a lot of searches (i.e. in top search queries table) but not driving traffic to your website (i.e. not in top search query clicks table).
In the example above, we can see that the top search query that returns a listing for this particular website, is 'ashburton', however that doesn't feature in the the 'search query clicks' table.
In this case we would want to see what page on our site is returned on Google for the search 'ashburton' and work out why the listing is not attracting people to click on it. Perhaps the title or description tags, or even page content may need work to make the listing more attractive.
Either way, it's an opportunity to rectify the problem and increase traffic to the site.
Page Analysis
This page shows you how Googlebot sees your website, including content on your website, and links from external sites to yours.
You want Google to be in no doubt as to what your website is about, and since one of the main factors helping Google decide on this is the content of your website and the links coming into your site, this page can tell you if your link anchor text, and site keyword density is correct.
The first table, Phrases: in external links to your site, shows you the anchor text links from external sites being picked up by Google. Ideally you want each one of these external links to reference your most important keywords.
If you see a lot of links without your keywords in the link text, or you don’t have any level of consistency across the board, it could be time to put in place a policy when exchanging links with external sites.
The next table Keywords: in your site's content shows you the top 100 keywords that Google has picked up from the content on your website. If relevant keywords to your business are not showing at the top of this list, it's time to rework your website content.
The third table is Keywords: in external links to your site and ranks the keywords in the anchor text of links from websites that link to you. Again, if your keywords are not showing up here, it's time to formulate a plan to get them in there.
Links Tab
This section is useful for seeing how many links from external sites Google has picked up. Your homepage is generally the most 'valuable' page on your website, so you would hope to see most external links to be pointing there.
Click the number of external links next to a particular page in that table and you will see a full list of all external sites linking in to that page, and when the link was last found.
In Search Engine Optimisation terms you want high quality, relevant websites linking to you (ideally one way links). If you haven’t got them, it's time to look at a program of quality link building.
Within this section you can also see the internal linking within your site. This is useful to see the internal 'weighting' you are giving to certain pages. The more links you have internally to a particular page, the more importance you are telling Google to attach to it.