In order to sleep, Mildred not only relies heavily on sleeping pills, she also relies on little earphones that she puts in her ears, that constantly plays music, entertainment, news and talk that her society channels in. They are just like earbuds, but wireless, and Bradbury refers to them as Seashells--probably in reference to how if you hold a seashell up to your ear, there is the continuous sound of the ocean waves roaring. These are just the same--there is non-stop news, entertainment, and mindless talk streaming constantly from these earphones. As Montag walks in the first night, he sees Mildred in bed, listening:
"And in her ears the little Seashells, the timble radios tamped tight, and an electronic ocean of sound, of music and talk and music and talk coming in, coming on on the shore of her unsleeping mind."
So, even as she rests, Mildred is surrounded by noise, by constant entertainment, just like she is during the day with her t.v. walls. Montag's society uses these seashells for two purposes. The first is to control information, and hence, thought and potential rebellion. If they are the ones controlling what information you get, they can tell you whatever they want, giving only one perspective, and painting a rosy picture so that people are never discontented. They also use the shells to relay important information. For example, when Montag escapes at the end, they send a message through all of the seashells for everyone to look out for him, and to turn him in if they see him. They automatically have a huge civilian army at hand, through the use of the seashells. Secondly, if people are constantly "plugged in," they don't have any spare time for their minds to be on their own. If people never have silence, they never think, and so never have the kind of discontented thought that come from meditation.
Mildred stays "tuned in" so much that she really has no mind of her own. In this sense, she is a perfect citizen of her society. I hope that these thoughts helped; good luck!