A pull request is a process which can merge new code into existing code.
"Software Engineer John was tasked to add a new logo to the website, when he was done he submitted a pull request of his feature branch into his organization's github repository for the website so that his team members could approve the changes before automation (like Github Actions) deployed live as a new version of the website."
It's a request to the owner of some reference in a Git repository to pull in some changes from some reference in some (possibly other) Git repository. You can do this via email, but centralised Git hosts like Github have their own interface to this basic workflow.
I agree the naming is misleading - it's not actually a request to pull anything - it's a request to merge someone's branch into another. This is known as a merge request on several other platforms.
"Software Engineer John was tasked to add a new logo to the website, when he was done he submitted a pull request of his feature branch into his organization's github repository for the website so that his team members could approve the changes before automation (like Github Actions) deployed live as a new version of the website."