Mobile-First indexing has to do with Google’s preference for indexing the mobile version of a page, as opposed to the desktop one.
Now, if your site is a responsive website, this is not going to be too much of a concern, because a responsive page is one that’s said to responsively adjust it’s display to match that of the viewport (the display area) of the device.
Nowadays, I believe most site-building platforms and WordPress themes have a responsive aspect to them.
Recently, during the December 10th, 2021 Google SEO Office-Hours, Google’s John Mueller was asked a question, the answer to which had to do with mobile-first indexing.
At around the 14-minute, 6-second mark, a participant explained her situation and asked a question. (This was part of a segment that involved a handful of questions.)
This video is queued to start playing at the appropriate position.
“So, also about the crawling issues. Since our crawling rate is back to normal, we noticed that our crawl requests from smartphones are recovering much faster than desktop. Could you shed some light on it? Any possible reasons behind this?”
John’s response was:
“I don't know. It sounds like what would be expected with mobile first indexing, that we crawl a bit more with mobile. I don't know if your specific site has already moved to mobile first indexing.”
The participant confirmed that it has been moved to Mobile-First, to which John replied:
“Yeah. But then that would be normal, that we just crawl more with mobile and then you would see any changes faster there.”