When presented with a (relatively) complex pitched sound, beyond just frequency extraction, your brain does additional processing to identify harmonic patterns, i.e. sets of frequencies where all of them are integer multiples of some fundamental frequency. This is an important part of our pitch perception. Because of this complex processing there is not always an obvious relationship between the spectral content of a given sound, and the pitch that a listener assigns to it.
There are techniques to combine sounds (combination tones and others) such that listeners will assign a lower pitch to the resulting combination than either of the individual sounds; the fundamental of the pitch of the combined sound is not physically present. This "missing fundamental effect" is somewhat surprising since for most sounds, it is the frequency of the lowest harmonic that determines the perceived pitch.
"Virtual pitch" seems to be a term coined by some music theorists in their attempts to describe the combination tone effect, as well as othersome features of (musical) sound perception, e.g. degree of consonance, and is consistent with the well known missing fundamental phenomenon. This theory includes the idea that the brain attempts to assign a "virtual pitch" to sounds, by looking for relationships between the spectral components. To my knowledge this term only applies to ideas that build upon those originally presented by Terhardt in the 1970's, i.e. it reflects a particular school or approach to this kind of analysis.