First check your broadband speed:
https://www.broadbandspeedtest.org.uk/
Recommended: at least 0.5 Mbps download
https://support.google.com/youtube/answer/78358?hl=en
However, YouTube offers several quality levels for videos. The lower numbers (360p) indicate that the video is smaller and uses less bandwidth, but is also less detailed. The more detailed the video (480p, 720p, or 1080p), the more bandwidth it takes to stream. Choose the highest video quality that allows you to stream without repeated stops and starts.
If you still experience issues try contacting your ISP to see if they can help.