The term antenna gain is confusing, and it is more correct to use the term directivity. An antenna is a passive element, and as such has no gain, since it does not amplify the signal. What the antenna can make is to concentrate the radiation to a certain area of the space, but we must understand that the higher the gain, the narrower the beam of radiation.
Using the analogy of the sources of light, a bare light bulb will be able to illuminate an object at a given distance. If instead of using the bare bulb we use a reflector, we can further illuminate the object, but we will leave the rest of the room in darkness. If we use a quality flashlight, with a parabolic reflector, we can concentrate even more the light beam (more “gain”), illuminating better the object, but we will need to focus precisely the object in order to get it illuminated.
Returning to the antennas, if we use a moderate gain patch antenna (8dB), the radiation is concentrated in a beam of about 60 °, allowing us to cover a large area of flight. If we want more gain, to increase flight distance, and we use for example a 24dB parabolic antenna, the beam width will be only 8º, implying that we have to keep the antenna fully focused on the plane. The figure below shows the flight areas with each of these antennas as an example:
To understand the radiation pattern of an antenna, the most intuitive way is using a three dimensional representation of it:
However, usually in the datasheet of an antenna we will more often find a polar representation of the radiation pattern. This is just making two “cuts” in the horizontal and vertical plane in the 3D representation:
On the other hand, and to measure more accurately the antenna gain in a certain direction, sometimes we use the Cartesian representation. It consists simply in “unwinding” the polar representation:
Associated with the radiation pattern we find the concept of beam. It refers to the area of space to / from which you can use the antenna, and is defined as the area where the gain exceeds the maximum antenna gain minus 3dB. Or in other words, is the area of space where the antenna emits at least 50% of the maximum power (which is the power emitted in the direction of maximum gain).
This implies that maintaining good antenna orientation is crucial, since we may be losing up to 3dB flying in the outer limits of the beam rather than at its centre.