What is a bad request?

Bad request are requests that returns 404/410 error. (It will show a 404 not found page)

Why bad requests?

Bad request are often caused by Broken links. Websites and blogs are often change its contents, links,and move its resources from one location to another location.
or you may have deleted resources that are linked in your pages.

How does if affect PageSpeed/Performance

When browser download your pages,and resources linked in the pages,(any scripts,stylesheets,fonts and images or any other resources that needs to be downloaded to render the page.)

And If any file is not found or returning 404/410 not found errors, browser will likely request it again, to check whether it can be downloaded anyway or to make sure the file is not exist, this process is called round trips. it will not only affect PageSpeed but also performance.
And if the round trips are for resources that are needed for subsequent JavaScript or stylesheets, it will affect rendering of the page.

Solution / Recommendations

To find broken links in your Website or Blog , Use any of broken link finder service that are available for free in internet. There are many free services available to find broken links in your pages.
After finding broken links, update it with the links or delete any reference to it.