More videos at the original post, but I would like to highlight these videos:

• How do vaccines work? Kelwalin Dhanasarnsombut, Ted-Ed (2015) Good general introduction.
• How fast can a vaccine be made? Dan Kwartler, Ted-Ed (Jun 2020)
• mRNA vaccines A slightly technical but nonetheless approachable explainer of how mRNA vaccines work (the basis of both Pfizer-BioNTech's and Moderna's COVID-19 vaccine).

And not to forget, Wikipedia has an excellent article on the current state of our COVID-19 vaccines.