Strateia
Strateia is greek for military service (n lit. trans, n ref.). In particular it was used in connection to the duty of certain "stratiotic" families, to provide military service in excange for tenure of "military land", also called "strateia".
Origin
(find better ref) The origin of this system is not entirely clear, but it likely stems from the Byzantine Empires loss of land and revenu following the Islamic conquest of Egypt and Syria. After these losses the Byzantine Empire likely began to expect its soldiers to supply atleast some of their own equipment, to compensate them the soldiers were given small grants of land to support themselves and their families.
Terms of service
(expand) Strateia was hereditary and was passed along within the family, it seems that, as far as possible, efforts were made to keep a particular strateia within the same extended family. The provincial commander was responsible for keeping muster rolls of the men available for service, he was also responsible for ensuring that said men were fit, and had sufficient equipment. Likely this envolved periodic mustering and drilling of the stratiotic troops.
Decline
(need ref) The strateia system seems to have declined somewhat towards the 12th century, along with the thematic system, as more and more stratiotic farms were expected to provide tax in liu of military service. (find ref)
References
(expand) Economic Expansion in the Byzantine Empire, 900-1200 by Alan Harvey