This word always appears in a birkat mitzvah, a blessing recited over the performance of a commandment. (However, some other brakhot have this word in them.) The suffix "-anu" means "us." (Similarly, "-einu" means "us.") By removing the suffix, we are left with the root that gives this word its meaning.
Kof-dalet-shin (KDSh) is a very familiar root in Hebrew. Kadosh, kaddish, kiddush, kedusha, kod'sheinu, yit'kadash, m'kadeish are all based on this root and appear multiple times in prayers and other texts.
KDSh is usually translated as sacred or holy. Indeed, that is what it means, but we really don't know what those English words mean. We associate them with something Godly, but how a person, place or thing becomes holy is generally not easily explained.
It may be helpful to understand that the opposite of kodesh, the noun, is chol. We usually translate chol as profane, which gives the impression of something inappropriate or dirty, as in "profanity." But what it really means is usual or everyday – nothing out of the ordinary. Something which is kodesh, which is other-than-chol, is separated out of the ordinary, set aside for different status. Certainly, when it is set aside by God (kid'shanu, the word of the moment), that segregated thing takes on a special aura. After all, to be chosen by God out of everything usual is a special privilege.
I know that the notion of being "chosen" makes a lot of us nervous. If the brakhah ended here, I might share some of that concern, but I hasten to remind you that just because we Jews were chosen by God for a purpose does not mean that others were not chosen for another purpose. We should rejoice in our selection, not be embarrassed or uneasy because of it.
So, finally, a translation of kid'shanu: "set us apart for sacred purpose." Take this moment to breathe in the prestige that comes with the implications. Next we'll see just how much of an advantage it really is.