Being the only one of its kind.
Note: Be careful and refrain from using adverbs to modify unique, such as very unique, the most unique, extremely unique. Unique means unique. One exception: almost unique.
But consider this contrary view from Dictionary.com:
Many authors of usage guides, editors, teachers, and others feel strongly that such “absolute” words as complete, equal, perfect, and especially unique cannot be compared because of their “meaning”: a word that denotes an absolute condition cannot be described as denoting more or less than that absolute condition. However, all such words have undergone semantic development and are used in a number of senses, some of which can be compared by words like more, very, most, absolutely, somewhat, and totally and some of which cannot.
The earliest meanings of unique when it entered English around the beginning of the 17th century were “single, sole” and “having no equal.” By the mid-19th century unique had developed a wider meaning, “not typical, unusual,” and it is in this wider sense that it is compared: The foliage on the late-blooming plants is more unique than that on the earlier varieties. The comparison of so-called absolutes in senses that are not absolute is standard in all varieties of speech and writing.
Strictly speaking, unique means “being one of a kind,” not “unusual.” Hence, the phrases very unique, quite unique, how unique, and the like are slovenly. The OED [Oxford English Dictionary] notes that this tendency to hyperbole—to use unique when all that it means is “uncommon, unusual, remarkable”—began in the 19th century. However old it is, the tendency is worth resisting.
But who can demand responsible use of the language from an ad writer who is loose enough to say, in a national advertisement, that a certain luxury sedan is “so unique, it’s capable of thought”? And what are we to make of the following examples?
—This year the consensus among the development executives seems to be that there are some fantastically funny, very exciting, very, very unique talents here” (Time).
—Residents of college basketball’s most unique unincorporated village were in place yesterday afternoon, the day before their Blue Devils will face North Carolina” (N.Y. Times).
Arguably, our modern culture lacks and does not want absolutes, in intellectual life or in language. But stick with the uncomparable unique, and you may stand out as almost unique.