Agogic accentuation is that which is not bound up with the regular pulsation of the music (the 2 beats in a measure, or whatever it may be), but which is called for by the nature of any particular phrase of the music. The first note of a phrase is often felt to suggest a slight lingering which confers the effect of an accent and this is one example. Similarly a leap to a note lower or higher than those that have preceded, or a strong dischord proceeding to a concord, suggests a slight effect of accentuation (by lingering, or by pressure, or both) and there are other examples.
The complementary term to 'agogic accent' is 'dynamic accent' (see dynamics) (i.e., accent of force), which implies the normal and regular rhythmic accentuation of a composition.
In a wider sense, 'agogic' covers everything connection with expression – ralentando, accelerando, rubato, the pause, accent of the kind above described, etc.