No, it's not a holly, although it does look like one.
This is one of the most common woodland understory shrubs in Eastern North America, occurring from Quebec and Ontario down to Texas. It is present in a wide array of habitats, on both low ground and in the mountains, and it seems to prefer damp places. It is a shrub that does very well indeed in considerable shade.
Sometimes it's hard to distinguish a large "shrub" from a small "tree," and this plant is sometimes in between. Normally, though, it gets to about 6-7 feet tall. Its leaves are smooth and dark green and shape-wise are fairly boring. In the autumn, though, the leaves put on a terrific show, becoming bright yellow. Its flowers appear early in the spring, before the leaves. The flowers are quite small and yellowish, crowded into small clusters up and down the stems. This species is dioecious. That is, individual plants are either male or female, as the flowers are unisexual. The flowers of "male" plants produce only pollen; "female" plants produce ovules, and, ultimately, a one-seeded, fleshy fruit. The fruits are brilliant red and quite conspicuous. Various birds like to eat the fruits and so scatter the plants throughout the habitat they are in. There's more natural history, too: This plant is a favorite food source for the caterpillars of one of our most spectacular swallowtail butterflies. All that said, you might want to investigate this plant as a resident of your garden. (Remember that it is the female plants that make the red berries.)
This species is related to a number of other aromatic plants, including sassafras, camphor tree and red bay. All of these plants are placed into the laurel family or "Lauraceae," which also includes the true laurel and avocado.
One of the old-timey common names for this shrub is "Benjamin-bush." I've tried to figure out how it got that name, and here's my idea: The whole plant is aromatic and pleasantly fragrant. One of the compounds producing this fragrance is an organic substance referred to as "benzoin," which is found in a number of different plant groups. The name "benzoin" was also applied to a fragrant gum used medicinally. Now, since our Mystery Plant has a long history of folk use as a medicinal plant and is in fact a source of the compound benzoin, many people began calling this plant "Benzoin bush." But that got gradually corrupted into the name "Benjamin bush," which was perhaps a bit less clinical than using the chemical name. However that name became established, the plant has been used as a source of tea and for medicinal tonics. And for flavorful toothpicks.
(NEWS FLASH: There is a relatively new plant disease out there now called “laurel wilt,” known now from the coastal counties of the Carolinas, Georgia, Alabama and all of Florida. It kills members of the laurel family, including native species such as red bay. Our Mystery Plant is susceptible to this disease, as are other species in the same genus. This is a serious problem now for ecologists and forest managers. You will probably start hearing more about it, unfortunately.)
[Answer: “Spice bush,” Lindera benzoin]