The visual representation of features on a map is called symbology. ArcMap has the flexibility to symbolize map features based on category , by quantity, by a feature's attribute, or something else. Also, symbology can be chosen from a variety of visual effects, including solid colors or outlined areas for polygons; circles, squares, and other symbols for points, and solid or patterned lines.
In ArcMap, the current symbology of a map layer is displayed in the table of contents on the left side:

Notice that most of the layers in the example above are shown by just a single symbol, but the "parcels" layer is symbolized by category, and the "tracts" layer is symbolized by quantity. For the single-symbol layers, the symbology can be quickly edited simply by clicking on the symbol, which will open the Symbol Selector window, allowing you to quickly change the symbology.:

To access more comprehensive symbology options for any layer (including the category- or quantity- based layers), right-click on the layer name, choose Properties..., and select the Symbology tab at the top:

The column on the left allows you to choose whether the layer features should be symbolized by a single symbol, classified by category or quantity, or labeled with charts. In this example, a layer of census tracts contains population density data, which can be used to color the various features of this layer according to density. To do this, the Quantities heading is selected, and the Graduated colors option is chosen. The Value: menu is used to specify which data field contains the population density data. If desired, the normalization, number of breaks, and color ramp can be specified as well. As these values are determined, the generated symbology is updated in the area below. Other ways of symbolizing the layer are specified using simiar methods through this window. Click OK to apply the changes to the map.
For more information about adding and editing visual elements on maps, see our Presentation Maps tutorial.