A king-worthy man of the extended royal family
According to the Medieval Sourcebook
Aetheling or 'æþeling' is an Old English word compounded from æþel or aethel meaning 'noble' and ing meaning 'belonging to' and therefore quite obviously means 'belonging to a noble family'. The oldest known written form of the word being apparently in the related language Old Frisian which has the very similar 'etheling'.(Aetheling is the most common representation of the word in Modern English but other variations include ætheling, athling or ethling etc.)
It is possible that the word was used at one time in this literal sense to denote any person of noble birth, but when the word appears in written records it appears to be used in a more restrictive sense, denoting individuals of strictly royal birth. For example the Anglo-Saxon Chronicle records the deaths of the aetheling Ealdberht of Sussex in 725 and that of Cynric aetheling of Wessex in the year 748. (Remembering of course, that the Anglo-Saxon Chronicle was composed in the late ninth century and its use of the term 'aetheling' in these contexts may well reflect contemporary usage of the term rather than any eight century practices.
From the tenth century it is clear from references in the Anglo-Saxon Chronicle that aetheling was used by the rulers of Wessex, who at the time were extending their control over all the kingdoms of the English, to specifically refer to the sons and daughters of the royal house of Wessex; what in modern terms would be a prince or princess.
Hence for the year 1013 refers in the plural to the aethelings Edward and Alfred (the sons of Aethelred who was king at the time) being sent abroad to Normandy for their own safety.
Later 'Anglo-Saxon' Law also defined the wergild, that is blood price or worth of an aetheling at 15,000 thrymsas, or 11,250 shillings; that is, same as that of an archbishop but only half that of the king himself.
It's use did not entirely disappear with the Norman Conquest; aetheling was occasionally used by Norman kings to designate the heir to the throne most notably with William, eldest son of Henry I, who was commonly known as William Aetheling. It was in this sense that the later Welsh kings, particularly those of Gwynedd borrowed both the concept and the name and coined the word 'edling' to describe the designated heir to the kingdom.
There is also a theory that the surname Alleyn or Allen is derived from the word aetheling. But then there is also the contradictory theory that it comes from the tribal name of the Alani.
SOURCES
The Anglo-Saxon Chronicles translated and edited by Michael Swanton (Phoenix Press, 2000)
Extracts from Anglo-Saxon Law at
http://www.yale.edu/lawweb/avalon/medieval/saxlaw.htm
The 1911 Encyclopedia Britannica at
60.1911encyclopedia.org/A/AE/AETHELING.htm
A Brief History of the Allen Surname
http://history.vineyard.net//allen/srnm.htm