Why An isotropic radiator is a mathematical fiction: a lossless point source that spreads power equally in every direction in three dimensions, so its pattern is a perfect sphere. No real antenna can do this, but it makes a clean reference for comparing gain, which is why gain figures carried as dBi are 'decibels over isotropic'. For example, a half-wave dipole in free space has about 2.15 dBi of gain because it concentrates power into a doughnut shape rather than a sphere.
Watch out The choices describing a calibrated physical antenna used for field measurements are wrong because an isotropic radiator cannot be built; real reference antennas are dipoles or standard gain horns, whose gain is itself stated relative to isotropic.
Isotropic = imaginary perfect sphere of radiation. dBi means 'gain over that fiction'; a dipole is 2.15 dBi.