Learn Russian: Мой брат учится на первом курсе, его специальность — лингвистика. - My brother studies in the first year, his specialty is linguistics.

The verb учиться is used to describe where or how someone studies, or their general status as a student. Because we are talking about his year of study (на первом курсе) and not a specific subject he is taking, we use учиться. If the sentence instead said "He studies linguistics," you would use изучает since that focuses on an academic subject: Он изучает лингвистику.

Doesn't курс mean "course" or "class"? Why does it translate to "year"?

In Russian universities, курс refers to your year of study as a whole, not a specific class. So на первом курсе means "in the first year (of university)". To talk about a specific class or subject you take, you would use a word like предмет.

Why do we use the preposition на for "in the first year" instead of в?

The noun курс is one of those words that always pairs with the preposition на when talking about what year of university you are in. So to say "in the first year", we use на plus the Prepositional case: на первом курсе.

Why is there a dash (—) between специальность and лингвистика?

Russian doesn't use a present-tense verb for "is" or "are". When you are stating that "[Noun A] is [Noun B]" (His specialty is linguistics), you put both nouns in the Nominative (dictionary) case and simply place a long dash between them in writing.