GIS stands for geographic information system, so by that term we could include any system which uses a geographical element and some associated tabular data. The wikipedia version states that a GIS is a system to capture, store, manipulate, analyse, manage and present all types of spatial and geographical data. This definition doesn't mention anything about computers and so could refer to both manual as well as computerised GIS.
At this time only very large organisations could afford to use computerised geographic information systems. These systems were customised for specific applications involving teams of programmers using main or mini based computer systems. Of course all that changed with the arrival of the personal computer. The advantages of desktop computing was quickly adopted to computerise such common tasks as typing, drafting and more interestingly for geographers, computerised mapping. The personal computer gradually allowed many quite complicated tasks to be accomplished without learning how to touch type, have formal drafting skills and for mathematical tasks the spreadsheet took away the requirement for mental arithmetic. Besides making life easier the personal computer enabled many office workers to multi task doing tasks previously requiring specialist skills and in the process becoming more productive.
If you would like to further explore how GIS could help your organisation jps services offers one and two day training courses in QGIS, ArcGIS and MapInfo.