It told it was a network error, so I waited for about 2 days assuming that it would have to do something with the network, but my internet has been functional. I'm presenting the screenshot that I took now , I'm writing question from my mobile and there's no network problem as I'm able to write it , then what's the problem and how to fix it? I did a Google search but all the issues were 4 years back, every body is talking about gingerbread in those posts, I'm running Android lollipop!
If you're internet is otherwise working fine, it looks like it could be an issue with the YouTube App itself. Try clearing cache and data for the YouTube App. This will effectively reset the app back to default settings and you will have to log back in.
Go to Settings -> Application Manager -> YouTube -> Storage -> Clear Data and Clear Cache.
Hope that helps!