The Creative Commons came about as an alternative to traditional copyright. They developed several legal licenses (below). While each license has its own set of rules, they also give a lot more freedom than traditional copyright, and they're written in plain language, so they're easier to understand.
This license lets others distribute, remix, tweak, and build upon your work, even commercially, as long as they credit you for the original creation. This is the most accommodating of licenses offered. Recommended for maximum dissemination and use of licensed materials.
This license lets others remix, tweak, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms. This license is often compared to “copyleft” free and open source software licenses. All new works based on yours will carry the same license, so any derivatives will also allow commercial use. This is the license used by Wikipedia, and is recommended for materials that would benefit from incorporating content from Wikipedia and similarly licensed projects.
Items come into the public domain in a variety of ways. One option is for creators to "dedicate" their items to the public domain. This simply means they choose to waive their copyrights. The CC0 license refers to items that have been "dedicated" to the public domain.
To find CC-licensed videos on YouTube, enter your search term, and click the Filters dropdown menu. In the fourth column (Features), you should see an option for Creative Commons:
If you want to download one of these videos, you can use ClipConverter or a similar tool.
Vimeo hosts many Creative Commons videos, too. Search for a video on your topic, and then select More Filters on the left. You'll then be able to limit your results by CC license. If the original uploader has allowed it, these videos will include an option to download.
Some videos can be downloaded - look for the Download button below the video: