Download videos from YouTube
To view the video
See also: How to download youtube videos on android

If you're looking for an application to download YouTube videos directly from your Android tablet or mobile phone, you can make use of the TubeMate application. 
Prerequisites

Configure your device to download third party applications. In order to install an application that is not on available on Google Play, you must configure your device:
Go to "Settings> Security"
Go down to "Device Management" and check the box to "Unknown sources"

Download and install TubeMate

Download TubeMate from your Android tablet or phone.
Once the file is downloaded, open the notifications panel ( or go to Settings> Storage> Downloads)
Click on the tubemate_1-5.apk file
Click on "Install" to begin the installation of TubeMate
Click Open to run the application.
To view the video

Go to Settings> Storage> Photos /Videos
Click on the video to start playback.