The goal of all directional antennas ("antennae"?) is to redirect energy into the desired direction.
For example, look at the ubiquitous Yagi antenna:
(image from CISCO)
In this case, there is one element behind the radiating element which is know as the "reflector". This acts as a mirror to direct that energy to the forward direction. There are also a number of elements in front of the emitter, called director(s), which focus what would be "sideways radiation" towards the front.
Note that the reflector and directors are parasitic. That is, they aren't driven, and only affect the radiation pattern based on their geometries.
So, when you look at a radiation pattern that shows back and/or side lobes, those lobes represent the energy that's left over from the attempts to direct it forward.