What is Directivity in a Coupler?

The Directivity in a coupler is the ratio between the input signal at the coupled port and the unwanted reflected signal at the coupled port. It is a measure of how well the coupler isolates two opposite-traveling (forward and reverse) signals at the coupled port.

This might sound confusing, so let me illustrate this using a diagram. See the figure below of a regular 4-port directional coupler. Port 1 is the Input, Port 2 is the output, port 3 is the coupled port and port 4 is the isolated port (which we ignore for this explanation). An input signal is divided between the coupled port and the output port with a small amount of power going to the coupled port and a large amount of power going to the output.

Now let's assume that the output is not well matched and there are some reflections - since couplers are reciprocal devices, the reflection from port 2 travel back towards port 1, part of this reflected signal is also coupled to port 3. The ratio of the wanted incident/input signal from port 1 (Input port) to the coupled port 3 of the coupler to the reflected signal from the output port (port 2)  which is coupled to port 3 is called directivity.

So when we say a coupler has a high directivity, this means that the reflections from the output port will cause less interference at the coupled port.