The read more block is used when you want to include a short introduction on your blog homepage & archive pages, and then link the reader to the remaining part of the article.
With Gutenberg, you can now edit the "read more" text for each post, and do so directly in the editor.
Edit "Read More" Text
After adding a "read more" block, simply click on the text in the middle of the dashed line, and update it.
When you view your blog's homepage, you'll notice that the "read more" text has been updated for that post.
The only other option with the "read more" block is for hiding the teaser before the "more" tag. When someone clicks from your homepage (or an archive page) through to the single post, you can optionally hide the content located before the "more" tag.
In most cases, I would not recommend this. It assumes that the reader always read what they saw on the previous page. If they didn't, it's like they're starting the story a few paragraphs in.