I submitted a research paper to a journal on 30th July 2015 and its status went 'under review' on 19th August 2015. I did not receive any communication from the journal, so I sent a gentle reminder on 11th Dec. 2015. Unfortunately I did not receive any response again. I then waited until 29th Jan 2016 and sent a reminder email again. Fortunately, the editor replied with "Your paper has been partially reviewed and we are waiting for remaining reviewers' response." The editor assured me that they will encourage the reviewer to submit the response.
Now, the status of the paper has changed from "Under review, date 19th Aug. 2015" to "Under review, date 2nd Feb. 2016".
I do not know what should I comprehend from this change in date?
When the status remains the same, but the status date changes, this often indicates that some of the reviewer comments have been added to the database and the editor has started accessing the database to view the comments. This also corroborates with what the editor has mentioned in his email to you. Probably, one of the reviewers has submitted the review while the others have not yet done so. Once all the reviews come in, the status will change to "required reviews completed."
My guess is that the reviewer they were waiting for has withdrawn or been dropped and a different reviewer been assigned. There are other internal actions that might cause the same sort of visible change as well, but all of them likely signify progress toward receiving your response.
I have experienced such situations as an author, reviewer, and editor. Generally, the reason for such change is that due to delay in reviewer's response or unable to provide review on the paper due to lack of sufficient knowledge in that area. In such case, editor assign a new reviewer in order to review the paper. Normally, each paper must be reviewed by at least 2 independent reviewers, and some editors (like me) prefer 3 reviews so that it becomes easy to take appropriate decision in case any two reviews contradict. Also, if the editor already have received a review or two, he/she asks assigned reviewer to provide review strictly within the review period defined by the journal. I hope you will get the reviews of your paper within the review time of the journal (after Feb. 2'16).