Mrs. Elvsted is describing C. Eilert Lovborg in those lines.
Mrs. Elvsted is married, however, she got involved with Lovborg somehow, a recovering alcoholic she was taking care of, who in turn was tutoring her children in history. Hedda, the protagonist of this text, notices that there is something going on between Mrs. Elvsted and Eilert Lovborg, and starts questioning her about that. That sentence above is one of the things Mrs. Elvsted says about her influence over Eilert.
