Gain
Gain is how much energy an antenna concentrates in its best direction compared to a perfect sphere. A 30 dBi antenna is 1,000 times more sensitive in its main beam than an isotropic radiator. High gain means long range; it also means narrow beam, so you must steer carefully.
Beam width
The angle within which the antenna's gain drops by 3 dB (half power). A 1° beam at 100 km covers about 1.75 km — that's your azimuth resolution. Larger dishes give narrower beams.
Polarisation
Horizontal, vertical, or circular. Rain returns are strongly polarised; aircraft returns less so. Weather radars use both polarisations to tell rain from hail. Stealth coatings are sometimes polarisation-selective.
Side-lobes
No antenna is perfect. Energy leaks out at angles other than the main beam — these are side-lobes. A high target lit by a side-lobe can look like a low target in the main beam, confusing the system. Good antenna design pushes side-lobes 30 dB or more below the main beam.