The description of a vessel which has movement through the water, frequently written as 'under weigh'.
Moving, as opposed to staying still. "We left the mooring and got under way at 0600 hours."
not at anchor or attached to the shore or aground; commonly used to mean moving through water
Anchor is up, lines are let go and ready to move.
A vessel is under way according to the navigating laws, "when she is not at anchor, made fast to the shore or aground." Generally speaking, it means that she is proceeding on a course.
A vessel in motion is under way.
when the anchor has been weighed or the lines cast off. Strictly speaking, a vessel can still be under way even though stopped, as long as she is not connected to the land