Search Analytics can be found under the 'Search Traffic' section and provides details of the keywords that drove clicks to your website, based on data for up to the last 90 days. The difference with Google's version is that you can filter the data to put extra context around the keywords, such as filtering by country to see keyword popularity based on country, which can be useful when carrying out keyword research for websites that service more than one country.
In Keyword Planner, formerly known as the Keyword Tool, you can get search volume and traffic estimates for keywords you're considering. Unfortunately, when Google transitioned from Keyword Tool to Keyword Planner, they stripped out a lot of the more interesting functionality. But you can make up for it a bit if you take the information you learn from Keyword Planner and use Google Trends to fill in some blanks.
The cost is only a one time payment…no monthly fees, which is fantastic if you’re on a budget, and you get lifetime updates and some truly excellent training videos as well as some very useful built-in tools. I’ve also tried other paid keyword tools such as Market Samurai, Wordtracker, Jaaxy, and others, and let me tell you this….none of them come close to Keyword Researcher Pro for value and ease of use.
What are people looking for on your site? These terms are keywords in the vocabulary of your actual audience and should definitely be added to your keyword list. Do not forget to look at the keywords people filled in that didn’t get any results: this was stuff people were expecting but didn’t find. You can look into the results of your internal search in Google Analytics at Behavior → Site Search → Search Terms.
If you're a regular blogger, these are probably the topics you blog about most frequently. Or perhaps they're the topics that come up the most in sales conversations. Put yourself in the shoes of your buyer personas -- what types of topics would your target audience search that you'd want your business to get found for? If you were a company like HubSpot, for example -- selling marketing software (which happens to have some awesome SEO tools ... but I digress ;-) -- you might have general topic buckets like "inbound marketing," "blogging," "email marketing," "lead generation," "SEO," "social media," "marketing analytics," and "marketing automation."
As for the history of the company, as I explained, I created Long Tail Pro back in 2011. At the time, I was creating tons of niche sites and was doing alot of keyword research and content creation. I was trying to figure out what types of keywords would rank quickly in the search engines, specifically Google, and I was frustrated with the other keyword research tools (in particular Market Samurai) out there.