Basically, Google shows the autocomplete suggestions whenever you start typing anything into Google search box. It is in Google's best interest to show the most relevant keywords in the autocomplete suggestions. Keywords that would help Google to retrieve the most relevant websites and help users find the most relevant content for their search query.
I just have the free version right now so I don't know all that the pro one can do. But even the free version has A LOT of tools you can use, I haven't even figured them all out yet. But one that I have used is their Content Optimizer. You can take a new or existing content piece of yours, and compare it to one of your competitor's pieces on a similar topic, and see where you might be lacking based on the keywords that are used in each piece.
The relevant keywords that you target with your ads will bring the right audience to your website. Showing your ads to people that type relevant keywords will result in higher click-through rate (CTR), lower cost-per-click (CPC) and higher conversion rates for your business. As a result, you will spend less money on advertising and generate a better return on investment.
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.