When molten rock is below the Earth's surface, we call it "magma". When it reaches the surface, depending on its mode of eruption, we call it "lava" or "pyroclastics".
Below the Earth's surface, magma bodies rise through the crust due to their bouyancy. In the lower part of the crust, because the crust is hot and "plastic" (pliable), magma bodies push aside and melt their way upwards.
When the magma bodies reach the shallower sub-surface, the existing rock is cooler and more brittle. This is when the process of "stoping" (rhymes with "roping") takes place. The rising magma body slowly fractures and forces aside the host rock(s). Often during this process, fragments of the host rock will break loose and become incorporated into the magma. If the magma is not hot enough to completely melt the incorporated fragment, it is preserved as a "Xenolith".
In the case of this xenolith, it is fairly small, with a maximum dimension of about 5 inches. The host rock is the Elberton Granite, from Elbert County, GA and the xenolith is a biotite gneiss.
The presence of the xenolith is referred to as an "inclusion" and using the Concept of Inclusions as articulated by James Hutton and Charles Lyell, without knowing the radiometric ages of either rock, we know that the xenolith is older than the host rock, as the xenolith was solid when it "fell into" the molten granite. [This is a brief glimpse into the concept of "Relative Age Dating", wherein we seek to establish a sequence of events without knowing radiometric ages.]
[As a further aside, at any give time, most magmas are probably not 100% molten, but rather a mixture of solidified minerals and still-molten minerals. The darker-colored minerals generally crystalize first, as the magma gradually cools. This progression is presented in the Bowen Reaction Series.]
When visible due to difference in color, sometimes individual crystals "xenocrysts" can be preserved in lava flows and solidified magmas ("plutons" or intrusions), having been "plucked" from older rocks as the lava/magma moved through.
[If nothing else, I have given you several new words to use in playing "Scrabble". "Xenolith" or "Xenocryst" would be worth a lot of points.]
Granites, being intrusive igneous rocks, only become "available" for study at the surface by way of faulting and/or erosion, as they form thousands of feet below the surface. The Stone Mountain Granite, of similar age to the Elberton Granite, is estimated to have been 10,000 feet below the surface when it solidified 300 to 325 million years ago. BTW, there are xenoliths exposed, in various places, on the weathered surface of Stone Mountain.
So, when you walk past a stone building facade, if you see a distinctly different mass of rock surrounded by "matrix", this may well be a xenolith.