Great video that explains the difference between the three different types of YouTube video.
Public - does what it says on the tin.
Unlisted - only those who have the link can see it.
Private - you can nominate the email addresses of up to 50 people. YouTube will helpfully send them an email telling them. They need to have a YouTube account set up in the name of that email in order to be able to view via the email. The downside is that you cannot withdraw the invitation - even if you remove their email access. They have the video within that email.