A great many physical systems take the form of a particle packing. The structure of such systems is often characterized through the study of local order. The current thesis makes progress towards a formal understanding of this physical phenomenon. It is demonstrated that particle packings cannot have global order without also having local order around every particle. A formal definition for local order parameters is proposed and an information-theoretic quantity that satisfies this definition is derived. This quantity is approximated with a simple coefficient $E$ that depends only on the number of neighbours and different bond angles associated with a particle. By generalizing $E$ to $n$ particles, a metric model of the space of three-dimensional coordination geometries is conceived and a taxonomy that is consistent with geometric intuition is recovered. An application of $E$ to an open problem in glass physics is considered. In particular, the variance of $E$ is used to characterize short-time structural relaxation in Kob-Andersen-type mixtures. This variance is found to be nearly composition independent at the onset temperature of glassy dynamics. It is also observed to behave like a heuristic measure of glass-forming ability, which could prove useful when exact methods are intractable.
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