When your site or post is an index that means your site or post is on Google. Ranking depends on the quality content, Authority, and many factors. Google needs some time to rank on the 1st page in the SERP results.
You should see it start to rank primarily for it’s name and/or the company name. Some long tail text should start to rank within a few weeks, assuming you aren’t taking any other action to promote the site.
That’s assuming it’s all spiderable, hasn’t been noindexed (IE you aren’t blocking crawlers) so that it’s fully accessible by said crawlers
After entering the URL into the index, the content immediately receives a search rank (position in search results), which depends on the content including search engine optimization, originality, and trustworthiness.
First a page gets crawled – that’s when Google reads the page and understands what’s on it.
Indexing comes after that, where it’s placed somewhere in Search Engine Results Pages (SERPs). Indexed means it’s somewhere on Google, but this might not be the first page, or the first 10 pages of a Google Search Result.
It could take time, or it could take changes for the SEO (most of the time you’ll tweak things a lot to get it to #1). There’s a whole lot that contributes to where it gets on Google, and sometimes if you’re copying content from either your own site or someone else’s then google will Crawl, but not Index your site and it’ll tell you (sometimes) what the issue is, and you’ll have a “Crawled – not indexed” issue.