A social share occurs when your page URL is pasted into a social media platform.
A user may copy and paste your URL into their social media feed or use a share function that you have installed on your web page. This generates both a link and a content element in the social feed and these may assist in generating referral traffic from the social platform.
When your URL is shared to a social media platform, either the actual links is shared, or a shortened link may be generated. Both tend to gain the “nofollow” attribute, so cannot directly benefit from the social media page or site’s own ranking strength. This is because the “nofollow” requests the search engine to not pass through the link to your site. This is just a request, not a demand, nor a fail-safe way to prevent a crawler from passing through the link. But Google will typically honor such requests.
The link therefore can’t pass page-rank to your page for Google organic search, however, the link may appear in your link profile in Google Search Console, and is likely to add positive weight to the profile. This is all conditional on the social media page being open to crawling by Google.
But, this is not really how your website can gain any SEO benefit. It may gain the referral traffic, but not SEO.
There’s plenty that disagree with me on this.
Where I do think you get an SEO benefit is when social shares have a flow-on effect of other shares outside the social network, or when the website becomes a brand-search target and gains a lot of click-through traffic simply from having become more well-known via the social channel.
Here’s what Ron Dod concludes about it on Search Engine Journal back in mid 2017: https://www.searchenginejournal.com/social-media-seo/196185/
Even if social media isn’t a direct Google ranking factor, it is one of the best ways to promote content and be found online. Which is, ultimately, what SEO is all about.