This paragraph is telling you about the verbs used in British and American English when talking about which subject you are involved with at university. The subject that you will gain a degree in when you finish your course. (Note: I am a British English speaker)
If I am currently at university and plan on receiving a degree in Physics when I finish successfully then, in British English, I would say:
"I study Physics (at X university)" or "I am studying Physics"
"I do Physics" or "I am doing Physics" (Less formal. Probably most common for casual conversation amongst university age speakers)
"I read Physics" or "I am reading Physics" (This one to me sounds very posh. I have not heard it used much at all even while at university, mostly I have heard it from older speakers and from the game show University Challenge. Maybe it is used more at places like Oxford and Cambridge university. I would generally avoid this usage unless you're sure it will be appropriate and use 'study' if you don't want to use the informal 'do'.
For American English, I would say:
"I study Physics" or "I am studying Physics"
"I major in Physics" "I am majoring in Physics"
My knowledge of specific usages in American English is limited so I don't know if either of these sound more natural or have more specific usage. (Perhaps someone can clarify in the comments). I believe you can also say "I am minoring in Physics" if physics is the lesser part of your 2 part degree.
Note: In American English, they would usually refer to a university as a college.