You have to tap the button with the three vertical dots again to bring up the menu.
Then select Quality and you will be given four options: Auto (Recommended), Higher Image Quality, Data Saver and Advanced.
If you need to reduce your data usage, just click Data Saver to make sure your monthly data is not being used up too quickly.
The higher picture quality setting looks like 720p is the maximum resolution it will go to.
The data saver seems to be maximum at 480p, but can be up to 144p when offered.
If you want to ensure that YouTube always shows videos in data saver mode, set this as the default streaming option in the Settings section of the YouTube app.