what does motion for an order directing abandonment mean?

Answer 1

That's a nice way of saying, "Your Honor, would you please tell this yo-yo to get the heck out of my house?" or something along those lines.

Answer 2

A motion is a request to the court, asking the court to do something, or to order one of the parties to do something.

An order directing abandonment -- what that means would depend on the context. I haven't seen that term, but I can only imaging it would either be asking that one of the parties abandon some claim (similar to a motion to dismiss) or asking that one of the parties abandon some claim to some property they putatively own.