A scalar value is a single component that can assume one of a range of values. An example of this is temperature. In contrast, a vector value has more than one component. An example of a vector value is a direction, composed of x, y, and z components. A scalar field is an arrangement of scalar values distributed in a space.
Typically, scalar field data being visualized is not continuous (as the original scalar field is), but is composed of a set of discrete sampled values. The sample spacing may be regular, forming a grid, or the sample spacing might be irregular, with varied spacing between samples values.
The sample values themselves will be limited to some finite range, due to limitations in the measuring equipment or restrictions on the simulation that created the values. Both the range of possible sample values, and the significance of the values themselves, vary with the application. For example, if a scalar field of atmospheric temperature values is used for aviation flight planning, the range of values is bounded to the values possible in the atmosphere. If the field is used for flight planning in winter, the values of greatest interest are right around the freezing point of water, since airframe icing is a major concern. In summer, higher temperatures mean lower aircraft performance, so unusually high temperatures are of greater interest.
When visualizing data, the exact values of the data are not as important as the relationship between values. Data visualization is used to gain insight into the data set, and expose relationships between values that might not be apparent in the raw data. As a result, intuitive, but less exact, representations of data values are often used.