Theoretical models can never fully represent the total complexity of the real world, but can only include certain aspects that are important for solving a certain question or problem. This is the whole idea behind creating models. One only includes that which is necessary and leaves out what is of no, or neglectable, influence (one hopes) on whatever is under study. Often, most of the aspects that are included are approximated and/or idealised.
Mechanical properties of a material are defined by the masses of, and interactions between, particles on a molecular scale (one could go even smaller, with quantum mechanics, or whatnot). However, the scales of most systems under review in mechanical and civil engineering (and many other everyday situations) are much bigger than that. For these systems one usually dispenses with looking at the molecular level and pretends that on a larger scale these materials are continuously spread out in the physical space. This is what one calls a continuum model.
A property that is locally attributed to the continuum (for example, the density) is in fact the result of the contributions of the molecules in a small space. The space should be large enough to contain enough molecules for the sum of their contributions to be statistically stable; on the other hand, it should be small enough in relation to the scale of the system under review to be able to speak of the properties defined at a single point of said system.
This results in these properties being able to be interpreted as functions of the continuous physical space. These functions are sometimes called fields, for example, the field of temperature, pressure (scalar fields) or velocity (a vector field).
Support write-up for Fluid mechanics
Sources:
An adaptation of an excerpt from one of my college textbooks - node your homework
July 8, 2001
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