Hir is a short word for "His/Her" or "Him/Her". It fulfils the need in English for a gender-neutral pronoun for situations where someone's gender is unknown at the time of writing.
Instead of writing the awkward sentence "Where is his/her file?" write "Where is hir file?".
Many other languages (such as Cantonese, Chinese and French) have a word that means "him/her" or "she/he". There is no easy way to shorten (s)he, so I accept "(s)he" as a good enough construct. Proposals for a gender-neutral pronoun have been one of the most common elements of English reform.
There are many wild suggestions out there to fix these problems, hir is one of the most textually aesthetic. Its drawback is that there is a tendency to pronounce it exactly the same as "her".
"It". Almost universally considered too impersonal to use for humans of unknown or irrelevant gender.
"They" and "their". Most the time, the use of the word "they" in a singular way will suffice but sometimes this causes ambiguity if, in context, it might be referring to a plural number of people.