Loudspeaker directivity refers to how the sound from a loudspeaker is radiated into the surrounding environment. It describes the speaker's ability to radiate sound in a specific direction, and how this changes as a function of frequency. Constant directivity means that the loudspeaker's ability to radiate sound in a specific frequency is constant as a function of frequency.
Ideally, a loudspeaker should have a flat and extended frequency response, because this results in the most natural and accurate sound reproduction https://support.dutchdutch.com/frequency-response/.
A loudspeaker's frequency response is usually specified for the sound that is radiated straight ahead, which is generally called on-axis. The on-axis sound is the sound that travels the listener's ears directly. However, your loudspeaker radiates sound in all directions, and each direction comes with its own frequency response.
The off-axis frequency response curves are almost equally important as the on-axis frequency response. That's because your loudspeakers are placed in a room with reflecting surfaces. Sound that is dispersed in all directions bounces around the room and at some point reaches your ears. Good loudspeakers radiate sound evenly across a wide range of angles.
A speaker's directivity refers to the relationship between the on-axis frequency response and the frequency response of all other axes. Constant directivity implies an equal frequency response shape independent of angle.
Loudspeaker directivity can have a significant impact on the sound quality and the listening experience. Ideally, a loudspeaker should have constant directivity, or directivity that changes very gradually as a function of frequency. This helps to ensure that the sound is perceived accurately and consistently by all listeners in the room.
Additionally, well-controlled directivity can help to reduce room reflections and minimize the effects of the room on the sound quality.