A GIS is a mapping tool which links information about where things are with information about what these things are like. Unlike a paper map where "what you see is what you get," a GIS map can combine many layers of information, most of which are not visible at first sight.
To use a paper map, all you need to do is unfold it. Spread out before you then have a representation of cities and roads, mountains and rivers, railroads and political boundaries. The cities are represented by little dots or circles, the roads by black lines, the mountain peaks by tiny triangles, and the lakes by small blue areas.
Just like on the paper map, a digital map created by GIS will have dots, or points, that represent features on the map such as cities; lines that represent features such as roads; and small areas that represent features such as lakes.
The difference is that this information comes from a database and is shown only if the user chooses to show it. Beside the information on where cities or roads lie, the database contains further information like, how long the road is, and even how many square miles a lake occupies.
Each piece of information in the map sits on a layer, and the users turn on or off the layers according to their needs. One layer could be made up of all the roads in an area. Another could represent all the lakes in the same area. Yet another could represent all the cities.
Each GIS map displays some of these layers, depending on what information is needed. For an example, these data layers can include features of water, flood risk zones, digital ortho-photos, zoning designations - even the locations of community disaster volunteers.
The advantage of a GIS over paper maps is your ability to select the information you need to see according to what goal you are trying to achieve.
For example, a business person trying to map customers in a particular city will want to see very different information than a water engineer who wants to see the water pipelines for the same city. Both may start with a common map - a street and neighbourhood map of the city - but the information they add to their own working map will differ.