Why is it that complicated words in a language never cause problems, but simple words do? I mean, no foreigner who studies Russian ever messes up a sentence with the phrase дезоксирибонуклеиновая кислота in it, but Americans who speak Russian misuse the word класс all the time.¹ Let's get to the heart of the matter. First of all, the word класс has multiple meanings that we will address over the next couple of weeks. Today we'll start with its most physical meaning, which is classroom, like the classrooms you find in a grade school or high school:

The trouble with the word for college-age Americans comes from the English usage “I am going to class.” In English the phrase means something like “I am about to attend the regularly scheduled event by which knowledge is passed on to me.” Even if your class is not meeting in a regular classroom, we still use the word class; for instance, “Today the professor is holding class in a conference room at the museum.” The sentence «Я иду в класс» means “I am going to the classroom.” It does NOT mean “I am going to class” in the normal English meaning. For that purpose one says “Я иду на занятия.” Notice that занятия is a neuter plural noun, but despite its plurality we will usually translate it as a singular in English, although sometimes the plural sounds okay as well:

¹ Дезоксирибонуклеиновая кислота = deoxyribonucleic acid (DNA)