Calculating Beam pattern, Directivity of microphone array
You choose the weights the steer the main beam of the antenna in the particular direction you want - let's call this $\theta_s$ i.e. steering angle. Now, given that you are steering the antenna in a given direction you are also interested in the array's response to incoming signals from other directions. This is the directivity pattern and is a function of the angle $\theta$ of the source signal. For conventional beamforming (non-adaptive) the magnitude of the directivity pattern will reach a maximum when $\theta_s=\theta$.