Layers are an old concept from traditional cartography that used to involve printing information on transparent sheets of film and overlaying them to see how things interacted. Luckily for us GIS is the ultimate layering tool. Layers are the foundation of a GIS and allow for the visualization of vast amounts of data for many differing features and conditions simultaneously.  The diagram below from NESDIS shows how this works for us- we can take separate data files with our donor's addresses shown as points, add a layer of all the streets in our city, add another layer of all the property parcels, insert yet another layer that models the elevation of our region and finally a layer showing land use classifications and combine them in one document and then manipulate each layer to get them all to fit together so we can see how they all interact using transparency and different symbology. Imagine the size of the data table that we would be using to generate all this data for an entire city- it would be huge and impossible to take it all in let alone relate the different features and conditions together.

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Layers are the slices of reality that we use to represent real world things- be they weather patterns, terrain elevations, animal sightings, trails, public transport routes or any other 'thing' that exists on the planet. We can combine multiple features in our GIS to view them in relation to each other or to perform analysis on how things impact other features, how certain objects can travel to reach other objects and an infinite array of other calculations and analysis. The real power of GIS comes not so much from the cool program you load or the amazing data you collected or sourced- it lies in the ways you apply all of these things to the problem you have at hand.

Next recommended reading is the summary on Coordinate Systems- (how to read the numbers beneath your maps)