It's mostly about reciting knowledge/passages from memory. "Recitations" were a common practice in education before disposable writing supplies were readily available and were teachers' primary form of assessment. Students would learn new information, by reading it themselves or listening to a teacher/tutor/professor tell them, and repeat it back.

They could be whole class, as in A Visit to Boston Schools, (1856) the author describes:

... in another, the Hancock, for girls, a sister of the Quincy, our visit occurred just at recitation.The teacher gave a slip of paper to a gentleman present, requesting him to write on it the names of several cities or towns in some way noticeable. Meanwhile, he said to the class, "English kings." They at once repeated in excellent concert, "Egbert, Ethelwolf, Ethelbald, Ethelbert," down to Victoria.

Or individual as seem in college entrance exams - a young man was told what to recite... and recite they would for a panel or individual tutor. The author is likely referring to times Roosevelt had to meet with a tutor/professor to prove he was keeping up with the readings and learning what he was expected to learn. Charles Eliot, who would go on to be the president of Harvard, spoke about his role in persuading the Mathematics department at Harvard to shift from recitations to written exams in 1854. Other departments slowly followed suit.

And finally, it could be a large or small-group class discussion as describe by a 1921 professor in an essay on how she was updating the "outdated" recitation for the modern era.

The monopoly of the recitation by the more able and self-reliant students was the next problem to be attacked. This, too, was in part overcome naturally, for many weak and timid students found it easier to express themselves to other students than to recite to the teacher.