GIS stands for Geographic Information Systems (or more recently, Geographic Information Science). In simple terms, a GIS is a software package that lets you store, manipulate, create, and analyze geospatial data.
What is geospatial data? It is information in a variety of formats (boundary maps, spreadsheets, digital photographs or maps, satellite imagery, etc.) that has some component letting you know where it is on the Earth.
GIS software exists both in commercially produced and open-source versions. The commercial options have more functionality but can be expensive. Use whichever one you have or are comfortable with!
Neither Google Maps nor Google Earth is a true GIS, but they can perform some GIS-like functions (letting you create data, viewing layers, querying). Both are nice tools, and if your mapping needs are simple they may do the trick.