A magic wand is a staple in a witch's tool chest. The wand represents our power as creators in this world. When we create things with magic it is indeed a high Art.
The wand is a tool of invocation and also of astral "scribing." We scribe out certain magical words or symbols with our wands as a method of inscribing the causal plane with our desire.
Someone who may catch a glimpse of witch doing this magical scribing can easily misunderstand and think they are simply "waving their magic wand."
Your wand can be made of any material you decide is appropriate. Traditional woods are discussed in the lesson on tools in my free 18-week course in witchcraft called A Witch's Primer.
A Witch's Primer also includes an entire lesson on using working magic with your wand.