Expeditio refers to military service, and in particular to the obligation to serve in the army or at sea. The subject of military service before the Conquest is a complex one which has long been the subject of heated controversy, Domesday supplying most of the fuel.
In the Anglo-Saxon period the obligation to military perform service was inherent in the land and assessed in terms of units known as hides or carucates. Theoretically, every landowner could therefore calculate his military liability by totalling the number of hides he possessed, and royal officials could calculate the service due from the areas for which they were responsible in the same manner.
In practice, it cannot have been as neat as this. Domesday Book does provide some particulars. According to a famous entry in the Berkshire Domesday, every 5 hides had to provide one man-at-arms and the money needed to support him for his period of service. Similarly, Exeter 'gave as much service as 5 hides of land'; Malmesbury provided one man from every 5 hides; and 'Bedford answered for a half Hundred before 1066, and does so now, in [military] expeditions, [by land] and in ships.' Naval obligations were also detailed for Dover and several other boroughs, together with the financial support required. Even inland towns like Bedford, Leicester and Warwick owed this ship service.
By the twelfth century, military service appeared to be based on quite different principles, with tenants-in-chief responsible for quotas of knights, the knights themselves being endowed with knight's fees to support their military obligations. Whether this was the result of the deliberate introduction of a new, feudal system by the Conqueror, or whether the old arrangement based on hides evolved out of sight into one based on fees, has long been debated. An evolutionary rather cataclysmic interpretation is now generally favoured; clear proof of either interpretation is not available.
For more detail on the Anglo-Saxon system, see C. Warren Hollister, Anglo-Saxon military institutions on the eve of the Norman Conquest (1962); and Richard P. Abels, Lordship and military obligation in Anglo-Saxon England (London, 1988); on Anglo-Norman military service, see J.H. Round, Feudal England (1895); C. Warren Hollister, The military organisation of Norman England (1965); and John Gillingham, 'The introduction of knight service into England', Anglo-Norman Studies, vol. 4 (1982), pages 53-64; 181-87.