A contrasedative, as the name implies, is something that works to counteract the effects of a sedative.
In this book, we see this sort of a drug used on Millie Montag. Mildred took too many of her sleeping pills that night. A sleeping pill is, clearly, a sedative since it is meant to cause a person to calm down and be able to sleep. Since Millie took too many of those pills, she needed something to counteract their effect. This is what a contra-sedative does and that is why she needed it.
Once again, a sedative is something that calms you down and a contra-sedative counteracts that effect.
To begin with, contra means opposite or against while a sedative is a drug which is taken to induce sleep or enhance calmness. Combined, the two words form the term contra sedative which stands for a substance whose effects oppose the effects of a sedative. As explained above, the sleeping pills ingested by Mildred are the sedative that cause tranquility and sleep. However, she has overdosed on at least thirty pills and requires an emergency procedure before it is too late. In fact, one of the operators who attended Mildred’s emergency informed Montag that the overdose can only be rectified through a combination of two procedures failure to which a build-up of the pills in the blood would cause brain damage. The contra sedative was administered into Mildred along with the new blood and has the opposite effects of a sedative. Before the operators leave, they forewarn Montag that his wife would wake up hungry and that he should try and keep her quiet. The next day during breakfast, Mildred complains of a hangover like feeling and is abnormally hungry.