The most valuable use of AdWords for SEO is to research keywords. Keywords are the basis of any SEO campaign and even if you are an expert in your niche, you should always research keywords simply because users frequently search for quite unexpected keywords and keyphrases you as an expert will never think of. Needless to say, what matters most for high rankings is which keywords your target audience is searching for, not which keywords you as an expert think are most popular in a particular niche.
It is simple to use AdWords to research keywords. You can either enter the URL of your site or put in some seed keywords, the tool will then automatically generate a whole bunch of suggested keywords. Look at the results and shortlist all the keywords that seem relevent and have a decent global search volume.
You may want to rank well for ALL the generated keywords, but its best to focus all your efforts on a selected few. The idea now is to find keywords that are relatively easy to optimize and yet have a decent search volume. These would be the keywords with the least compitetion in Google. Go to Google.com and enter each of your short listed keywords (one at a time). It is best if you search for the exact phrase, so surround your keyword with double quotes. Note how many web results there are for each of the phrases. Now that you have collected the 'Number of web results' for each keyword, calculate competition ratio by divding it's 'Global search volume' by the 'Number of web results'. The keywords with the higher ratios are the easier ones to optimize.
You can now start a SEO campaign for your keywords however you'll see next, it might be much wiser to start an AdWords campaign instead.