Using media content that is protected by a copyright and hosting it on a personal website is considered copyright infringement and may be subject to fines. Embedding media content, such as YouTube videos that are protected by a copyright, is not considered a copyright violation.
Embedding is a way of sharing the direct link to the hosted source of the content, and YouTube offers an embed link with all content that is uploaded. It's up to the person uploading the material to disable the embed code or not. By leaving the embed code enabled, the user allows embedding by others.
For other uses of copyright-protected material, permission must be granted in advance. Copyright rules vary according to a variety of factors, such as the type, where it was published and length of term for the copyright to remain in effect. Once expired, the content belongs to the public domain and may be used freely on a personal website without purchasing or obtaining rights or permission. It is the responsibility of the user to find out what copyright, if any, the content is protected by.
YouTube is not responsible for granting permission to use content uploaded to its site, according to Google. There are other features offered by YouTube to help users find usable content that doesn't infringe on any copyright rules. YouTube's audio library provides music and sound effects that are free to use. Additionally, its video editor allows users to remix video content that falls under Creative Commons licensing.