What is a constant envelope modulation?
You've pointed out a very important distinction between theory and practice. In theory, as suggested by your book and in Fat32's answer, modulation schemes where all information resides in the phase of the signal, not in the amplitude, are called "constant envelope modulation". However, in practice our systems have finite bandwidth and instantaneous phase jumps cannot be realized. Consequently, in such cases the envelope will have dips where (theoretical) phase jumps occur.

Nevertheless, there are systems which really have a constant envelope. Such systems produce a (complex baseband) signal of the form

$$s(t)=Ae^{j\phi(t)}\tag{1}$$

where $\phi(t)$ is a continuous function of time. Such signals are well suited for extremely non-linear channels (amplifiers), and they are also more spectrally efficient than signals with a (theoretically) discontinuous phase.

Modulation schemes producing a signal as given by $(1)$ are called continuous phase modulation (CPM). Examples of CPM are continuous-phase FSK (CPFSK), and minimum-shift keying (MSK) and its variants (e.g., GMSK)