When watching videos on YouTube, it will default to the highest available quality (HD), which can use over 400MB / hour. Luckily YouTube has a feature to allow you to show standard (SD) quality video when you're using your mobile data, and then HD video when you are on Wi-Fi. Keep in mind that even at SD quality, YouTube can still use around 180MB / hour so if you want to keep your data usage down, keep an eye on how much time you spend streaming videos.
On your iPhone / iPad – In the YouTube app, go to Menu (three dashes) > Settings (the Cog Icon) > ensure “Play HD on Wi-Fi only” is ticked.
On your Android mobile / tablet - In the YouTube app, go to Menu (the three dots) > Settings > General > ensure “Limit mobile data usage” is ticked.