I understand that the content in an iframe is not considered part of the parent page. If you only embed a video on a page, the search engine might see this is an empty page and refuse to index the page.
In fact, I believe Youtube video provide the best user experience (faster video streaming and support all devices) compared to you host the video at your own server.
You can solve this problem by having a video transcript below the video, and put in more text content in the page.
If you are talking about your own video that you have uploaded to youtube, you could host that video from your site (upload your video file to wherever your site is hosted) and use the html video tag.
The video tag offers some interesting options as far as playback and controls, and allows for captions, subtitles, descriptions, and metadata that will be read by webcrawlers as being a part of your site.
W.E. Jonk: If you use that, G might serve your landing page instead of the YouTube one. ;
Jonathan Stiebel: Google see's videos from youtube, they own it. Everything is connected through their analytics, so if you want a post a video direct from youtube on your site, it can only do good.