If you consider which way the vortices are rotating you'll realise that there is an upward flow of air outside the span of the wing, and a downward flow of air behind the trailing edge of the wing. This downward flow must not be confused with the ordinary downwash. One difference is that the latter is allways accompanied by a corresponding upwash in front of the aerofoil, so that the final direction of the airflow is unaffected. But in the case of the wing-tip vortices the corresponding upward flow is outside the wing span and not in front of it, so that the net direction of flow past the wing is downwards. Therefore the lift - which is at right angles to the airflow - is slightly rearwards, and thus contributes to the drag. This bit of the drag is induced drag.
In a sense, induced drag is part of the lift; so long as we have lift we must have induced drag, and we can never eliminate it altogether however cleverly the wings are designed. But the greater the aspect ratio, the less violent are the wing tip vortices, and the less the induced drag. If you could imagine a wing of infinate aspect ratio, the air would flow over it without any inward or outward deflection i.e. no wing tip vortices and no induced drag. Unfortunately, from a structual point of view, there is a limit to how large the aspect ratio can be. The greater the wing span the greater must be the wing strength; the increase in weight counterbalances any gained advantage. It's all about compromise.
TCF