Although we still use the term outlaw, we've long lost touch with the original meaning of the term, which was for someone to be placed literally outside the law and hence its protection. The practice was used among the Romans and persisted into many pre-modern societies in Europe. In England, the Latin pronouncement made when someone was outlawed equated them to a wolf, outside the human community and hence open to attack by anyone from inside it.
Making someone an outlaw was a popular practice in pre-modern societies because it removed the burden of prosecuting the individual from the legal authority. In the centuries before the advent of railways, modern communications and standing armies and police forces, the authority of the state was at most a passing phenomenon in most parts of Europe - rather than pursuing an individual itself, it was much easier for the state to outlaw someone and leave them to the tender mercies of their fellow citizens. In some cases it was prohibited to aid outlaws, and doing so might lead to being branded one yourself; killing them, meanwhile, was regarded as a social good.
Outlawry declined as the power of the modern state grew and states took on many of the prerogatives that they had formerly been happy to see exercised by someone else. Outlawry is a relic of a time when power was seen as being exercised over people much more than over territory, and so to expel someone from the protection of being one of the people in the political order was the harshest possible crime. With the rise of the sovereign nation-state, authority came to be seen as all-encompassing within a certain territorial area - and states took an increasingly dim view of anyone but themselves exercising violence within it.
The other main cause in the decline of outlawry as a concept was the strengthening of legal procedures and criminal justice systems which allowed modern states to extend their power legitimately. The Magna Carta, due process and habeas corpus all placed stress on the due rights of individuals to be tried and sentenced by state authority in a fair manner, rather than merely being declared to be wolves and hence effectively non-human. Gradually, over the centuries, this was the bargain that developed between modern states and their citizens - to always be placed within the protection of the law, but always to have to be in a state of complete subjection to it.