How is it possible to rank first for a keyword, when the keyword isn't written on the page?

[Jesssherl]

I noticed that one of our competitors is ranking in first position for a keyword but when looking on the page grader. The exact keyword is not used on the page at all (or in title, URL etc.). How is this possible, when other sites have content with those exact words?

[effectdigital]

Popularity and off-site factors, e.g: backlinks which have a high degree of association with the key term. What other people think about you online (and how they reference you) often matters more than how you shout about yourself (through your own content, which is biased)

[pilesofpillows]

They probably use it in their Meta Title and have enough LSI keywords or related keywords that Google clearly correlates them with the keyword you are searching for.  Also, I bet they have a good amount of quality inbound links and possibly some internal or external ones pointing to the ranking page that have part of or all of the keywords in them.

I would try and evaluate why Google thinks this is the best result in terms of quality and content depth, not simply if they have the exact keyword in the page copy or not.