This question is so big that I tried to find a good hub on it but didn't have much luck! So here goes....
Yes, for most financially successful content writers keywords are of primary importance and for me they're fundamental. The better you are at keyword research the more readers & money you'll earn.
People use keywords when they use a search engine to find information. They will type in a phrase such as "how to stop my swimming going green" or "cheapest place to buy vitamins in the UK" or "funny cat videos" etc etc.
The search engine's job is to find the pages most relevant and satisfying (think quality and reader experience) for a search query (ie: keyword phrase) in their index and display them in the search results.
The content writer's job (that's you) is to give both the search engine and the potential reader exactly what they are looking for. ie: the best page on the web about "how to stop a swimming pool going green".
So basic SEO is essentially making sure that the search engine knows that your page is about "how to stop a swimming pool going green" so that it is displayed on the first page of search results when a searcher types that phrase into the search box. We make sure the search engine knows this by ensuring that the phrase is in the title of the article and that the page content is tightly focused on the question.
To appeal to your readers your page needs to be written in a way that is suitable for your particular online audience ie: plenty of descriptive subheadings, easy to read and understand, useful images, tables and video when appropriate.
Many content writers will use a keyword tool, like the free one available from Google, to look at the rough amount of searches per month for a given phrase before they start writing on a topic. Why? Because in general the more searches (traffic) a phrase gets the more you can earn from it. A phrase that gets 100 searches per day or more is generally more profitable than one that gets 1 per day (this does depend on the type of phrase and whether people are looking for info or looking to buy something but that is for the next lesson!).
Unfortunately keyword research is not actually this simple because we also need to look closely at the websites that are already ranking on the 1st page of google for a phrase we're interested in to see if they can be beaten out. We also need to take into account whether the phrase is a "fresh" one or truly evergreen (again this is another lesson).