Ruach HaKodesh

Ruach HaKodesh is a Hebrew term:

Ruach (pronounced Roo-akh) - Wind, Spirit, Soul.
Ha - literally 'the', functions as 'of'¹
Kodesh - Holyness, sanctity

In Jewish thought, Ruach HaKodesh refers to a particular type of prophecy, traditionally the type that the Patriarchs received. It isn't what might be considered 'true prophecy' though.

While not clearly defined, it's clear that Ruach HaKodesh refers to a sort of Divine inspiration. The Midrash often refers to people as having seen something through Ruach HaKodesh, and much of the Old Testament is said to have been written through Ruach HaKodesh (But not the Torah -- Orthodox Jewish belief says that was written a much higher level of revelation).

It's unclear exactly how Ruach HaKodesh functions. The sources seem to make it some kind of inspired hunch -- like the Jargon File's zen. There's also a reference in the literature to Jacob not being able to 'use' Ruach HaKodesh while in mourning for Joseph, because it requires the user to be at peace.

At least one literal translation of Ruach HaKodesh is "the Holy Spirit", and when used in Christian theology it means just that. In fact, do an Internet search on "Ruach HaKodesh" and you'll mostly find Messianic 'Jewish' websites using the term to refer to the Holy Ghost in a Jewish-sounding way.

¹As Gritchka has pointed out, this isn't exactly true. However, it'll do without explaining Hebrew construct forms

http://www.shemayisrael.co.il/dafyomi2/megilah/points/mg-ps-07.htm
http://www.ohr.org.il/misc/eterni-7.htm
http://shamash.org/listarchives/mail-jewish/volume13/v13n39

Ruach (Roo-akh) Ha-Kodesh, a Hebrew term literally meaning Spirit of Holiness, is a level of inspiration that is just below that of Nevuah. According to the Rambam in the Moreh Nevuchim (Guide for the Perplexed,) this is simply an abnormally intense intellectual understanding, such that it is clear that it is from beyond you, but is still a purely intellectual understanding that can be understood by others. This is not he level of Nevuah, or true prophecy. All the books of the bible were written with Nevuah, but the Mishna and Talmud were written with Ruach HaKodesh.

This term is also sometimes used, in a (gramatically) very odd sense, by christian missionaries, to refer to the holy ghost. and more grammatically correct way to do this would be Haruach Hakodesh.