MyBB is not very optimized for search engines by default. One of the biggest problems is that it does not come with a robots.txt file.
Search engines will crawl all kind of stuff in your forum that makes no sense. Examples are the calendar, the archive, new reply pages and many more.
They will also find a lot of duplicated content in your forum because the same posts can be displayed in the archive, using a direct post URL and all kinds of thread URLs with lastpost or newpost.html additions. MyBB does not ship with canonical URLs by default so you’ll have issues here too.
My currently recommended robots.txt for MyBB with activated SEO-friendly-URLs looks like this: