They’ll show you information like how many external links the site has, the number of Facebook and Google+ shares, estimated visits per month, and its page authority. All of this is valuable intel that can give you insight into where your page could potentially rank against them, without needing to do more research with a separate tool or on another page.
Using the good ol' free Google Keyword Planner is great. But there is an alternate universe of Long Tail keyword phrases that live in Google's other database--namely, their "Autocomplete database." That's the database that is accessed when you're typing queries into the Google search box (notice that list of suggested keywords that pop up as you type?)
Although more and more keywords are getting encrypted by Google every day, another smart way to come up with keyword ideas is to figure out which keywords your website is already getting found for. To do this, you'll need website analytics software like Google Analytics or HubSpot's Sources tool. Drill down into your website's traffic sources, and sift through you organic search traffic bucket to identify the keywords people are using to arrive at your site.