Sometimes when I walk into the room where my bearded dragons terrarium is located, he waves an arm up and down in my direction.
Does he expect me to wave back to him?
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This is a pretty common thing for beardies, and definitely appears to be some kind of greeting.
The reasons that a bearded dragon will wave their arm is not entirely explained. However, it does seem to be a form of communication. A common belief is that arm waving is a passive message, to indicate submission when a larger or more dominant beardie is near by.
So, he is acknowledging your dominance, which is healthy; you're the one who knows where the food is. In this case, you don't really need to reply; he's essentially being polite.
However, they can wave for other reasons:
One meaning is species recognition. If a bearded dragon waves at another bearded dragon, it tells the other dragon that he/she is aware of their presence.
Alternatively, the age of your beardie can affect the meaning.
Young bearded dragons may do a slow "wave" with one of their arms to signal, "I'm just a baby! Don't hurt me!" Your young beardie may even do this when he sees you walking up to him if he is intimidated by you...
While this is a not-so-nice thought, he may grow out of it. We have to remember that even reptiles are not robots; they have moods and personality quirks too that change over time.
All in all, it can't hurt to wave back. A best, he'll be comforted (you're being submissive too), at worst he'll be confused. They wave back and forth to each other quite frequently, so he may well appreciate a reply, even if he isn't expecting one.
My beardie has always chosen to wave and mix in head bobbing. He will respond in kind when I am standing at least three feet from his home but gets very agitated if i approach after his initial greeting without signaling back. This has always led me to believe its a way to greet and communicate with friends and perhaps warn away or be alerted to dangerous creatures as they seem to not have the best eyesight for long distances, ie. the other side of my living room or about 25 feet.