I just posted this in a response to some questions in Etsy Success Team and thought I would copy it over here because I thought it might be helpful:
Etsy Search algorithm (the formula used to determine relevancy) is said to function like this:
First Etsy looks at the title for EXACT word phrase matches and lists those items as most relevant.
Second it looks for EXACT word phrases in the tags section and lists those matches.
Now, you have probably noticed that most of the listings in a relevant search DO NOT have EXACT keyword phrase matches in their title and maybe not even their tags and here is why:
Etsy also uses USER INPUT to determine relevancy. So, if someone searches for "crochet baby bib" and looks at 3 pages and clicks on a listing from page 3, that listing just got a huge bump in relevancy because someone found it relevant. Though the other listings previous to it were also relevant the one that got clicked became more relevant and jumped up to maybe page 2. It might have been what the user was looking for.
Now, the relevancy of being clicked does not just get a bump in a relevancy search. It gains relevancy if it is clicked on from any spot. If it is clicked on for a treasury or in the Newly listed section of the front page or clicked on from anywhere inside Etsy it gains relevancy based on its title and tags.
Renewing gives your item a small chance of being clicked on from different areas on Etsy. Renewing does not guarantee you a bump in relevancy just by renewing.
There are other aspects of the Etsy Search algorithm that they have not released and probably never will. The best thing to do is to make sure you have a very relevant title (mainly the first 3 words) and relevant tags. The better you are at describing the item in the title and guessing how a customer will search for your item the better chance you have of being found, clicked on and sold.
Forgot to mention that it is far better to work within a niche rather than in the general category. Example:
It is better to optimize for Crochet Baby Bib than Baby Bib. You'll find far less competition the more specific you get with your title and tags.