As a verb, to wet-nurse someone means to look after them far more than a grown person needs — to feed them, fix their problems, and follow them around as if they were a helpless baby. It is a complaint, almost always. A manager says "I can't wet-nurse you through every job" and means: you are an adult, do it yourself. A teacher might say a class has been wet-nursed for too long. The picture behind it is strong and a little rude, so it is not a polite office word; it is what someone says when they are tired or annoyed. English has several near neighbours here — spoon-feed, babysit, hand-hold, mollycoddle — and wet-nurse is at the harsher end of them. Note that the same spelling is also a noun with the older, plain meaning: a wet nurse (often two words) was a woman paid to breastfeed another woman's baby, a real and common job in the past, and that is where the criticism comes from. The verb is more common in British English than American, and it is not very frequent in either; you will meet it in novels and in speech more than in writing. It is usually written with a hyphen as a verb: wet-nurse, wet-nursed, wet-nursing.