Hebrew Bible refers to the textual canon of the Jewish Tanakh, which contains books that were originally written mainly in Hebrew. (There are two books, Daniel and Ezra, that have parts in Aramaic, but even they are written in the same Hebrew script.)
See the main article: Tanakh.
The Hebrew Bible includes the same books as the Protestant Old Testament, but not the deuterocanonical portions of the Roman Catholic and Eastern Orthodox Old Testament. The term Hebrew Bible does not impose a particular ordering of its books (as opposed to Tanakh and the Old Testament, each of which orders the books in different ways).
Section 4.3 of the Style Manual for the Society of Biblical Literature recommends the use of the term "Hebrew Bible" as a bias-free term in preference to the term "Old Testament" in academic writing. Other examples of recommended bias-free terms include the use of "Second Temple period" instead of "intertestamental period" and "deuterocanonical literature" instead of "Apocrypha".