A good question recently asked on the Wizards boards. (You’ll see it used in strategy posts a lot).
What does “basing” mean?
It means moving in to base-to-base contact with a figure. “Basing” is a lot simpler than saying “moving adjacent to”, especially when some people can’t seem to comprehend that “adjacent” in DDM means “base-to-base contact” rather than “within a creature’s Reach range”. (Sulaco’s explanation)
“Basing” a figure means that the figure cannot cast non-touch spells or use ranged attacks without first moving away – drawing an attack of opportunity for doing so – and so is an essential part of good play.
Personally, I prefer the term “engage”, but that might be just me. 🙂