MSK spectral efficiency explanation
In traditional FSK, the frequency separation between pulses is $1/T$, where $T$ is the symbol rate. This guarantees orthogonal pulses while maintaining a continuous phase. The phase is continuous because a pulse with the next higher frequency traverses exactly one more cycle than the one with the lower frequency (during one symbol interval).

However, you can easily show that in order to guarantee orthogonality between pulses, a frequency separation of $1/2T$ is actually sufficient. This is indeed the minimum frequency separation guaranteeing orthogonality. Now a higher frequency pulse traverses only half a cycle more than the pulse with the next lower frequency. The smaller frequency separation reduces the bandwidth compared to traditional FSK, whereas the probability of error remains unchanged due to the orthogonality of the pulses. This is why MSK is often referred to as bandwidth-efficient (compared to traditional FSK).

Note that for MSK to have a continuous phase the initial phase of a pulse must be either $0$ or $\pi$, depending on the phase of the previous pulse (because some pulses have a phase value of $\pi$ at the end of a symbol interval due to the minimum frequency separation of half a cycle per symbol interval).

This additional "phase encoding" inherent in MSK can actually be used in the receiver by applying the Viterbi algorithm. In this way, MSK can perform better than traditional FSK. It can overcome the 3dB loss of FSK as compared to PSK.

Also note that MSK can be viewed and implemented as a special case of offset keyed PSK (with sinusoidal pulse shapes).