A standing army is an army composed of full time professional soldiers who 'stand over', in other words, who do not disband during times of peace. They differ from army reserves who are activated only during such times as war or natural disasters. Standing armies tend to be better equipped, better trained, and better prepared for emergencies, defensive deterrence and particularly wars. 
The army of ancient Rome is considered to have been a standing army during some of Roman history, but especially the empire .
The first 'modern' standing army in Europe were the Janissaries of the Ottoman Empire, formed in the fourteenth century AD. In western Europe the first standing army was established by Charles VII of France in the fifteenth century.  The establishment of a standing army by King James II in 1685 in Britain and later the control of the British Army over the British Colonies in America was controversial, leading to distrust of peacetime armies too much under the power of the head of state, versus civilian control of the military, resulting tyranny.
In his influential work The Wealth of Nations (published 1776), economist Adam Smith comments that standing armies are a sign of modernizing society as modern warfare requires increased skill and discipline of regularly trained standing armies. Since the eighteenth century standing armies have been an integral part of the defense of the majority of more economically developed countries.
In Great Britain, and the British Colonies in America, there was a sentiment of distrust of a standing army not in civilian control. In Great Britain, this led to the British Bill of Rights which reserves authority over a standing army to the Parliament, not the King, and in the United States, led to the U.S. Constitution (Article 1, Section 8) which reserves similar authority to Congress not the President.