"Throw him in the dungeon. Why? Because I say so."
People who are arrested in civilised countries are generally brought before a court soon thereafter. There are usually rules to this: e.g. that the person must be charged in a court with a crime within 48 hours of the arrest, perhaps longer over a weekend.
The practice of detention without trial is the keeping of persons in jail without the intention of charging them with breaking the law, or bringing them to court to determine guilt or innocence, or even if there is any substance to those charges. Detention without trial is generally regarded as a bad thing.
Detention without trial is usually supported by a legal framework that allows this practice, normally with certain restrictions. After all, the unrestricted power to lock up people indefinitely without having to give reason is a hallmark of a repressive regime. Where detention without trial is practised without a supporting legal framework, it is fair to say that the country is not ruled by law. Where there is a legal framework that allows prolonged periods of detention before charges are brought, the country may be a Police state, since this is a tool that the police may use against any citizen whom they dislike.
Many countries, e.g. the USA and Australia, practice detention without trial on would-be illegal immigrants who are captured.
In the state of emergency of the end days of the Apartheid state of South Africa, the police were given the power to detain without charge or trial any person whom they thought to be a security risk, for up to 120 days.
There are grey areas for instance, is it detention without trial if the suspect can be held for 90 days before charges are brought? Is it still unacceptable if there is "judicial oversight" to determine that there is in fact a good reason to hold the suspect while more evidence is gathered? British MP's in 2005 found such regulations unacceptable, and voted against them, despite the best efforts of Tony Blair and company. A compromise bill, allowing for 28 day arrest was then passed. In 2008 measures were introduced to extend this to 42 days. Why this number was chosen is not clear, since there seems to be no evidence for it and plenty against it.