Organic keywords are simply the queries a page appears for without anybody paying for the placement. The phrase is worth being precise about because it marks a boundary: what you can influence by writing and structuring a page, as opposed to what you can buy. For an existing site the interesting thing is not the definition but the list, because almost every site already ranks for queries nobody deliberately targeted, and those are usually the cheapest work available.
Where your own list lives
Search Console's Performance report is the answer for any site you own. It lists the queries that produced impressions, with clicks, average position and impressions attached, over whatever period you choose. That is not an estimate of your organic keywords: it is a record of them, which is why it beats every third-party guess about your own site and why it is the first place to look rather than the last.
What to do with the top organic keywords once you can see them
Sort by impressions and look for two patterns. Queries with many impressions and few clicks are usually a title and description problem or an intent mismatch, and they can often be fixed without writing anything new. Queries sitting between the bottom of page one and the middle of page two are the ones where a modest improvement to an existing page moves real traffic, which is a much better use of a week than a new page from scratch.
The queries you rank for by accident
Every site has them: a paragraph aimed at nothing that happens to answer a real question. Treat these as evidence rather than as wins. If a page attracts a query it does not really answer, either the page should answer it properly or another page should, and the accidental version should stop competing. That decision is a clustering decision and it belongs in a record.
Organic against paid, briefly
The same query can be bought and earned, and the two behave differently: paid arrives the day you switch it on and stops the day you stop, while organic is slow, cumulative and not yours to control. Keyword lists for the two overlap but the selection rules do not, which is why a bid list is a poor starting point for a content plan.
Questions people ask about organic keywords
What are organic keywords?
The queries a page shows for in the unpaid results. Nothing is spent on the placement, so what you can change is the page and the site around it.
How do I find my website keywords?
Search Console's Performance report, for any property you have verified. It shows the queries that generated impressions, with clicks and average position, over the period you pick.
Why do I rank for queries I never targeted?
Because search engines match pages to intent rather than to a list you wrote. Accidental matches are useful evidence about what your page reads as.
Can I see another site's organic keywords?
Only through a third party's model of them, which is an estimate built from sampled ranking data. Your own are a record; theirs are a guess.