i stands for isotropic hear, dBi = isotropic dB. This comes from the antenna theory. In antenna theory, isotropic antenna is called something that can radiate radio waves in all directions at the same intensity. I really don't know why (maybe form some historical reasons) this is used, but you can't have isotropic antenna in real life, however, it is used as a base to calculate the real antenna directivity. So it s actually nothing else, but a number of dB compared compared to isotropic antenna (comparison, nothing else). Similarly you have dBm (power ration of dB compared to one milliwatt)
