Literally, the term is used to specify the time between interval (for example "change dressing q8 hours), however, in the context that you ask the term refers to how often you are on call overnight in the hospital. For example a strict q2 schedule would mean that you are on call every other day (Mon, Wed, Fri, Sun, Tues, Thurs, Sat, etc.); a strict q3 schedule is every third day (Mon, Thurs, Sun, Wed, etc.); and so on.
As far as actual hours that this entails, in general a call day starts when you report for morning rounds on the day of call and ends 24 hours later in terms of taking admissions, etc.; Yet, in most programs you do not go home immediately after the 24 hours is up, but end up going home anywhere from noon that day on, depending on the specialty and type of program (the exception I believe is Anesthesiology which mandates a 24 hours maximum if I recall correctly, or maybe that is my hospital only)
Hope this helps you