my immigration case status says in active review by immigration service officer what does that mean?

Active review by an immigration service officer means that the case is off the shelf and on someone's desk. How long it may take for the officer to actually finish the adjudication depends upon how many other active files the officer is working on. But it is always a hopeful sign when you learn that a file is in active review. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.

That means an immigration officer, often a supervisor, is reviewing the case file together with the recommendation of the initial reviewing officer.