She wants to sleep = Elle veut dormir.
Voudrait is the conditional form of the verb vouloir, thus the conditional mood "would like" in English.
What's the difference between voudrait and aimerait? I understand that technically the first translates to "would want," but in English that's a slightly different meaning to "would like"
"J'aimerais" is a little higher register of politeness and it is more like "it would please me" or "I'd really like."
Really they are very close though and both are polite when asking for things.