HPBW or half power beamwidth refers to the angular width between the points at which the radiated power per unit area is one half of the maximum.
Similarly FNBW (First null beam width) refers to the angular width between the first two nulls as shown in Fig 7.3. By the term beam width we usually refer to 3 dB beamwidth or HPBW.
Directivity and gain:
We have already mentioned that an antenna does not radiate uniformly in all directions. Directivity function 
describes the variation of the radiation intensity. The directivity function is defined as,
= 
If Pr is the radiated power, the 
gives the amount of power radiated per unit solid angle. Had this power been uniformly radiated in all directions then average power radiated per unit solid angle is 
.