Rarity in books is a more specific concept than it appears.
Age alone does not make a book rare. A seventeenth-century almanac printed in a run of ten thousand copies, widely distributed and widely kept, may be less rare than a pamphlet published in 1950 in an edition of two hundred that the author's family bought and destroyed.
The components of rarity are four, and they interact.
Edition is the starting point. First editions matter because they are the text in its earliest form, before revisions and corrections, and because the print run was usually the smallest. But not all first editions are equal. A first edition of a book that sold poorly and was never reprinted may be abundant. A first edition of a book that went through forty printings in its first year was almost certainly produced in greater numbers.
Provenance is the ownership history. A copy that passed through the hands of someone significant to its subject becomes an association copy: the thing moves from being a book to being an artefact. A copy of a poet's collected works annotated by the poet has a different order of value than the same edition in unread condition.
Condition determines what a book is worth at the point of sale, regardless of what it might be worth in principle. A first edition in worn, incomplete condition is a different object from a first edition in dust jacket, unread. The gap can be enormous.
The fourth factor is documentation. Rarity that cannot be demonstrated is rarity that cannot be sold at its true value. Provenance requires evidence. Edition points require bibliographic verification. The collector who cannot substantiate what they have owns a book; the collector who can owns a rarity.
Know what you have before you describe it to anyone else.