Diagram explaining how the directivity (directive gain) of an antenna is defined.  R (grey) is the radiation pattern of a typical directive antenna. It radiates most of its power in a narrow lobe oriented along the z axis.  Riso shows the radiation pattern of a hypothetical isotropic antenna| that radiates the same total power as the first antenna but radiates it equally in all directions.   Isotropic gain G is defined as the ratio of the power density S (in joules per square meter) radiated by the antenna in the direction of its main lobe (here the z-axis) to the power density Giso radiated by the isotropic antenna
G=SSiso{\displaystyle G={S \over S_{\text{iso}}}}
When the power radiated by the antenna is concentrated in a small angle about the axis, as shown above, the signal strength is greater than the power radiated by the isotropic antenna whose power is radiated evenly in all directions, so the directivity G is a measure of how concentrated the antenna's radiation is in one direction.
Own work
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