Induced drag is the cost of producing lift (basically what BeePee said). An actual wing cannot produce lift without also producing induced drag. Induced drag is not directly related to speed. It is related to angle of attack. In level flight, to fly slower requires a steeper angle of attack, which results in higher induced drag. When the angle gets too steep, the wing stalls producing little lift and a lot of drag, but this drag is mostly form drag, not induced drag. Since the airplane cannot maintain level flight slower than the stall speed (except when being sustained by thrust alone) there is no induced drag in this flight condition.

There are only two significant ways to reduce induced drag, high aspect ratio, and light wing loading. These both reduce the angle of attack required for a given amount of lift, thereby reducing induced drag. (wing tip design and planform also affect induced drag, but not nearly as much as AR and wing loading.) An actual wing design is a compromise depending on the desired flight profile and the relative importance of induced vs form drag at the design flight conditions.