Certificate errors are often due to security risks associated with particular websites. This can happen if your computer thinks that there may be virus or malware risks to your system by accessing a website. With YouTube, this shouldn't be the case, so you may just need to investigate some of your browser settings.
How to remove certificate error warnings when viewing YouTube:
Firstly, check that your browser is up to date. Even if it does not resolve this particular issue, it is good practice to make sure you have the latest version.
If you have an antivirus software running, look to see if that is what is causing the problem. If your security settings are too strict it may be that certain content is being blocked. You can usually adjust the general settings to remove the block, or else add YouTube as an exception which your AV recognises.
If all else fails, try downloading a different web browser to see if this solves the issue. You can import all of your settings and bookmarks from your previous browser, so it should be fairly straight forward.