Scarcity, condition, provenance and demand, in roughly that order. A knife is collectible when fewer exist than people want, its condition can be verified, and its identity can be established, usually from a tang stamp. Age alone does not make a knife collectible, and neither does a high original price.
Scarcity, meaning limited production, a discontinued pattern or an unusual variant. Condition, meaning unused, unsharpened and ideally boxed. Provenance, meaning the knife can be identified and dated, usually from its tang stamp. And demand, which is the one nobody controls.
All four have to be present. A rare knife nobody wants is not a collectible, it is just rare.
Age by itself. An ordinary well-used knife from 1965 is an old knife, not a collectible one. A high original price does not do it either; plenty of expensive production knives never appreciate.
Neither does a limited-edition sticker. See numbered and limited editions.
Buy condition and buy identifiable pieces. An unsharpened knife with a crisp stamp and its original box will always be worth more than the same knife carried and sharpened, and the gap widens over time.
And be honest with yourself about which knives are collection and which are users. See user versus collector knives.