1. Monitoring system health
2. Reporting on system health (response times, availability, etc)
3. Reporting on transaction volumes on the website
4. Analyzing customer sessions on the website to find any issues that may impact customer experience
5. Analyzing customer reviews of the website to find underlying issues
6. Incident management - review and address issues that affected single users
7. Defect management - review and document issues that require development work to fix
I'm sure the list could go on and on, but that is at least a good overview. Also, depending on the system for which your analysts skills would be needed, the actual output could differ as well. While extensive knowledge of programming languages was not necessary to be successful in this job, some knowledge and a willingness to learn at least the basics did come in handy when trying to figure out problems on my own.
I have done this type of work both on site with companies as well as in a remote worker situation. Since the majority of the work involves reviewing, analyzing, and reporting on data a face to face work environment is not always necessary. However, depending on the company you work for, additional project work could be involved in the position which could necessitate more in person meetings.