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The basic phase precession phenomenon is apparent when you look at the timing of place cell spikes relative to the hippocampal theta rhythm:

(Figure from Malhotra et al. 2012) Each spike is assigned a color based on the /phase/ of the theta rhythm (a component of the LFP or “local field potential”) at which it occurs. Note the smooth color change as the animal runs through the place field.

An important conceptual step is to extend this idea to what happens in a population of place cells which are all phase precessing:

(Figure from Skaggs & McNaughton 1996, which is well worth reading)