Because the full moon will occur only about 28 hours after the summer solstice, and the moon will be at the southernmost point of its orbit at that time, one of the lowest full moons for nearly two decades will be observable from our area.
The Moon orbits in an orbit slightly inclined from the plane of the ecliptic (the plane of the Earth's orbit), with an angle of about 5°. The Moon can therefore project up to 5° south (i.e. 10 of its diameter) of this plane. Because of the tilt of the Earth's axis of rotation, the ecliptic appears lower in the sky in some places and higher in others. The southernmost point is in the constellation Sagittarius. At the time of the June full moon, the Moon will be near this point and also at the southernmost point in its orbit. It will therefore be almost as low as it can be in our area during a full moon. In some places in our area, it will not rise higher than 10° above the horizon at the culmination!
The moon itself will not be any bigger or smaller than usual, just very low on the horizon throughout the night. However, people may find that the Moon appears larger at sunset or sunrise. But this is a matter of optical illusion - our brains compare the rising or setting Moon to distant objects on the horizon, making it appear larger than when it is high in the sky. But what is likely to be noticeable is the lesser brightness of our cosmic counterpart. At this low altitude above the horizon, the attenuation of light in the Earth's atmosphere will already play a role, as the rays travelling from the Moon to the observer will have to travel a longer path through the Earth's air, and this will scatter some of the light (especially the short-wavelength light) significantly. The Moon will therefore appear slightly fainter and probably more yellowish than bright white. Either way, this will be an ideal opportunity to photograph the full moon with some not very tall objects on the horizon or perhaps some storm clouds.
We will see such a low-lying full moon over our horizon again next year, specifically on June 11st, and we will have to wait until June 22nd, 2043 for another similar opportunity. It will therefore be a relatively rare spectacle.