Algebraic free response questions allow your instructor to ask a question that expects an algebraic equation as an answer. Unlike a short answer question these questions don't require your submission to exactly match the answer in the system, but rather your answer has to be mathematically equivalent to the correct answer on record (eg. X+1 is the same thing as 1+X). These questions are also not case sensitive.
Another use for this type of question is to ask for an interval or list response. The behavior is the same as the equation response type, but keep in mind that your answer should be in exact form, using fractions and symbols where appropriate.