Cocubines

First of all, in that era, they had no choice but to send their young daughters for emperor to pick as concubines. If they didn't, their heads would get chopped off -- it's the law. They must obey the absolute orders of the emperor.
Secondly, those parents whose daughters were sent to the palace were not just some normal person, BUT they were the government officials so of course they had to play the politics there.

Back then life expectancy was very short. Teenage was the beginning of adulthood. 16 was a common age for marriage so it was not gross. But as s.o. said, it was mainly because they had no choice than to obey an imperial edict... otherwise everybody in their household would have been killed...the daughter included. :(

Realistically and pragmatically speaking, yes its a power move, and a very important move that could set the course of an entire family or clan.

Sending a young and beautiful daughter is a good way to be in good standing with the monarch. And if said daughter gets the emperors favor, then it gives the clan benifit of being in the good side of the emperor but it also has an added protection. In that era, one wrong move not only can kill the man, but it could also decimate his whole clan,  a time when Ministries/nobles alike scheme against each othe. Thus, if they have a favored daughter to the king, then they will have the ears of the emperor, and they will not be so weak to schemes.they will not be accused as easily or their clan be destroyed easily, thus the protection. And on the flipside, having the the ears and protection of the emperor via favored daughter, can be used to scheme against other and they will likely get away with evil deeds due tp their daughter. 

But also remember, that during that time, it was somehow beliebed that emperors are desdendants of gods/dieties/dragons, thus sending their daughter to the harem is akin to having a holy sacrifice and can bring heavenly good lcuk

Except reasons that others mentioned,I think there is other reason too: as we know in the past women didn't have much value, they were objects that own by men. Even in some historical dramas, they mention that a woman is a man's belonging, it's their destiny and they should accept it. Even parents back then believed that daughters are useless and they should give them to others. Some people even trade their daughters for money or land,etc back then.  Even now there are some parents who sell their daughters in different ways.