Scheduling job interviews can be a nightmare. Between candidates who already work during regular office hours and interviewers who are swamped with a multitude of work tasks, interviews can sometimes occur at odd times. Although it's not usually anyone's first choice, the weekend may be the best time to interview for a job.
If the hiring company suggests a Sunday for your interview, this is likely due to the scheduling difficulties of a key interviewer. It may mean you will be seen by a relatively senior executive, which is a plus. When you are a job seeker, it's wise to agree readily to any unusual scheduling requests from the hiring company - you'll be seen as flexible and professional, two key qualities in a job candidate.
This unusual scheduling may have no bearing at all on the work hours you'll be expected to fulfill if you get the job. Then again, it could mean the company expects you to be flexible and available to work on weekends. Look for hints during the interview as to what kind of commitment will be required from you and the company's policies regarding work/life balance. If weekend work or being available in the evenings is a deal breaker for you, it's best not to accept a job offer from that company.
If you are having difficulties getting away from weekday responsibilities to interview for a new job, you might suggest a Sunday interview to the hiring company. However, this could be inconvenient for the interviewers, so don't insist. The interviewers should be sympathetic to your need for discretion, but may suggest alternate times, such as lunch time or after work in the early evening.
There's one other situation in which you might encounter a Sunday job interview. Mass weekend interviews sometimes happen when a company is launching a new location and looking for dozens of employees at the same time - usually for entry-level or unskilled positions. In this case, the company may hold a job fair combined with walk-in interviews. These events may be held on the weekend to allow maximum participation.