dBi is decibel above the gain of a isotrope antenna as a reference.

The isotrope antenna is a mathematical antenna with a radiation pattern of a perfect sphere.
From this background it is calculated that a dipole antenna has a gain of 2.15 dB referenced to the isotrope antenna.

• A dipole has a gain of 2.15 dBi
• A dipole has a gain of 0 dBd
• In the case of a yagi antenna with a gain of 14 dBd the yagi has 14 dB more gain as a dipole.
• the same yagi has a gain of 16.15 dBi

dBi is used for mathematical purposes and by commercial guys who want to add 2.15 dB more gain to the antenna they sell :-)