In our last session, the party came up against a troupe of outlaws who had seized control of a village and were using it as their headquarters to waylay, rob and murder travelers. The party received information from the king's foresters who, recognising them as adventurers, advised them that they would be within their legal right to apprehend the outlaws, the implication being that there would be no legal repercussions if the party went so far as to slay them and claim their property, even without waiting for the coroner to arrive. In this context the sentence, 'We're not officers of the law' was uttered, and so it seems some background on the way the law is enforced in our campaign world is in order.
There aren't 'officers of the law'. The closest thing medieval England has to a police force is the town watch, a handful of men who do their best to stay awake through the night and take appropriate action in emergency situations. There are only a few of them to patrol an entire big town, and they're responsible not only for making rounds to check for burglary and violence, but also to watch for fires and look out over the town walls in case of an invading army. For the rest of the time and for all other purposes, and for every purpose in the case of rural areas, communities are responsible for their own 'policing'.
Each free male, on reaching the age of twelve, is required to be sworn into a tithing, a group of ten households headed by a chief tithing man; the tithing reciprocally enforces obedience to the law among its members. If someone in the tithing is accused of a crime, the rest of the tithing is responsible for bringing him to justice (perhaps turning him in to the local bailiff or gaoler, or to the lord's retainers if they live on a manor). If they fail to do, they stand to be fined for more than they can afford to lose.
On a manor, disputes and trials are overseen by the manor court, in which the lord is often judge and jury with the power to execute those found guilty. Death by hanging is the most popular punishment--with drowning typically preferred if the accused is female--for all sorts of offenses from theft to murder. The only other common punishments are fines and being placed in the stocks. Incarceration is very rare, and grisly punishments like burning at the stake or being drawn and quartered are reserved mainly for extreme cases of religious heresy and high treason, respectively.
In a town, there are usually one or more magistrates, men of good standing selected by the king to act as judges in criminal matters.
Fines for such things as starting a fight vary by locality, always with heavier fines for drawing blood. In any case, anyone who witnesses an act of violence or theft is expected to raise the hue and cry, a signal to all in the vicinity to rush to help apprehend the perpetrator. The sound, whether made vocally or with the aid of some instrument, would be known and recognised by all who live in the area. There is a fine for failing to raise the hue and cry, as there is for failing to respond to it. All free men keep some form of arms depending on their status and what they can afford; they are required by law to be able to defend themselves and their country as well as arrest criminals when necessary.
In cases where the accused remain at large, they are generally given three chances to appear in court. If they fail to appear, they are declared outlaws the fourth time and can legally be beheaded on sight.
A complication that allows many criminals, particularly criminal bands, to remain at large and unpunished, is the practice of maintenance, whereby lords protect their criminal retainers. Our trial session gave the party a taste of this system when a knight hired them to investigate a different group of bandits; the knight was on a quest to make maintenance illegal. As it stands, the law is very selectively enforced, with those who lack political power keenly aware of their position; and corruption is rife.
The question was asked why the foresters themselves don't carry out justice, or at least help the party and claim part of the reward. The answer is that the king has appointed them to patrol his forest and hang poachers, not to risk their lives confronting dangerous bands of outlaws. Even if they wanted to join the party, the king would not be pleased if they abandoned their duties to do--and the political consequences would be particularly messy if the outlaws are under a lord's protection.
Finally, to expand on the foresters' mention of not needing to wait for the coroner: The coroner (from the Latin corona, 'crown') is an officer of the king who is supposed to be present before justice can be carried out. The coroner's duty is to assess the value of man's assests to determine what portion of his property should go to the king. As common law already allows for the lord or householder to claim the belongings of anyone who dies on his property, and death sentences pronounced on manor courts already ensure that the lord of the manor will receive the man's best beast, the coroner is necessary to make sure the king gets his due. When outlaws are apprehended, citizens are supposed to wait a maximum of forty days for the coroner to arrive, but this is often flouted when the situation is extreme.
Thus, the party are currently in that most coveted position of adventurers: They can kill people and take their stuff.