To understand tonicizations, let's first recall what modulation is -- a change in key, which means that the tonic (“doh”) has been changed. It is typically established by some kind of dominant-to-tonic progression (i.e., V-I or viio7-I and their inversional variants).
Sometimes, the modulation can be so brief that writers variously describe it as a “passing,” “transient” or “fleeting” modulation. In general, these so-called modulations introduce chromatic colours to the harmony without changing the overall tonic of the passage in question. A good example is when an imperfect cadence has its dominant chord preceded by the latter's own dominant:
I - ii6 - V6 of V - V (see also Ex. 17.1b and Ex. 19.1, or for a more extensive example, Ex. 17.4)
T PD D ---------------
Or, likewise in the case of an interrupted cadence:
I - ii6 - V7 - viio7 of vi - vi (see also Ex. 18.7e)
T PD D (T) ----------------
We refer to such relatively brief chromaticizing processes as tonicizations. To put differently, the chromatic chord involved converts a non-tonic scale degree into a local tonic. In the first example above, it is as if we have a V6 - I in the dominant key but put in context, we still hear second chord as a V, as part of an imperfect cadence. In the second example, locally we hear a viio7- i but in context, this is heard as part of an interrupted cadence--albeit chromatically-coloured.
As mentioned above, tonicization (like modulation) is typically established by some kind of dominant-to-tonic progression. In the case of V7/V - V, we say that "the dominant has been tonicized" and "the applied dominant is the V7 of V". In the case of viio7/ii, an "applied dominant substitute" is used to tonicize the supertonic, turning the supertonic into a local tonic as it were but we still hear it as a supertonic rather than as the tonic for the passage concerned.
Modulation and tonicization involve the same harmonic mechanism to establish itself, hence we may think of them as differing in extent rather than in kind.
Besides colouring the harmony, tonicizations can help to link chords very smoothly and even turn poor progressions into good ones. Consider the following:
I - ii - iii - IV - V
This otherwise weak progression (not to mention the series of parallel fifths it embodies) can be transformed with tonicizations thus:
I - V6/ii - ii - viio7/iii - iii - V65/IV - IV - V6/V - V (see various variants in Ex. 18.17 and Ex. 19.13)
T PD ---------------------------------------------------------- D -------------
Exercise 5 in Chapter 17 (p. 418) provides an instance of linking vi to V using V43/V.
Clarification
Applied dominants are also referred to as secondary dominants. This should not be confused with secondary chords, which belong to diatonic harmonies. The following categorization will help clarfiy:
Diatonic harmonies - consists of primary chords (I, IV, V) and secondary chords (ii, iii, vi, viio)
Chromatic harmonies - includes secondary/applied dominants and their functional substitutes