Bible Dictionary Definition of Unicorn:

Probably the extinct, two-horned gigantic Bos primigeniua, or aurochs. Possibly the one-horned rhinoceros. The original language indicates a wild bull of some sort.

The rendering of the Authorized Version of the Hebrew reem, a word which occurs seven times in the Old Testament as the name of some large wild animal. The reem of the Hebrew Bible, however, has nothing at all to do with the one-horned animal of the Greek and Roman writers, as is evident from De 33:17 where in the blessing of Joseph it is said; "his glory is like the first born of his bullock, and his horns are like the horns of a unicorn;" not, as the text of the Authorized Version renders it, "the horns of unicorns." The two horns of the ram are "the ten thousands of Ephraim and the thousands of Manasseh." This text makes a one-horned animal less likely to be what is being referred to.

The rhinoceros is a one-horned animal that matches the description where Reem is mentioned in the Bible except that it is unlikely that the animal in the Bible has one horn rather than two.

Considering that the reem is spoken of as a two-horned animal of great strength and ferocity, that it was evidently well known and often seen by the Jews, that it is mentioned as an animal fit for sacrificial purposes, and that it is frequently associated with bulls and oxen we think there can be no doubt that, some species of wild ox is intended. The allusion in Ps 92:10 "But thou shalt lift up, as a reeym, my horn," seems to point to the mode in which the Bovidae use their horns, lowering the head and then tossing it up. But it is impossible to determine what particular species of wild ox is signified probably some gigantic urus is intended. (It is probable that it was the gigantic Bos primigeniua, or aurochs, now extinct, but of which Caesar says, "These uri are scarcely less than elephants in size, but in their nature, color and form are bulls. Great is their strength and great their speed; they spare neither man nor beast when once; they have caught sight of them" --Bell. Gall. vi. 20.-ED.) clipped from Smiths

"The elasmotherium, an extinct giant rhinoceros, provides another possibility for the unicorn’s identity." Answers in Genesis

". . . could have been an aurochs (a kind of wild ox known to the Assyrians as rimu" Answers in Genesis

07214 reh-ame’ or reh-ame’ or rame

AV-unicorn 9; 9

1) probably the great aurochs or wild bulls which are now  extinct. The exact meaning is not known.