Keywords are important because they are the linchpin between what people are searching for and the content you are providing to fill that need. Your goal in ranking on search engines is to drive organic traffic to your site from the search engine result pages (SERPs), and the keywords you choose to target (meaning, among other things, the ones you choose to include in your content) will determine what kind of traffic you get. If you own a golf shop, for example, you might want to rank for "new clubs" — but if you're not careful, you might end up attracting traffic that's interested in finding a new place to dance after dark.
Advertising with Google won't have any effect on your site's presence in our search results. Google never accepts money to include or rank sites in our search results, and it costs nothing to appear in our organic search results. Free resources such as Search Console, the official Webmaster Central blog, and our discussion forum can provide you with a great deal of information about how to optimize your site for organic search.