This is more of a history question.
勇 is short for 乡勇, which roughly means "militia". They are temporary soldiers recruited from the local population in times of need, and are usually disbanded soon after. Soldiers wearing 勇 on their uniforms was a Qing dynasty thing though; they stood in contrast to the elite Banner Armies and the professional Green Standard Army, both of which could be lifetime occupations.
In movies, you might see Qing soldiers wearing uniforms with either 兵 or 勇 written on it. Those with 兵 would probably be from the Green Standard Army, which was usually employed as a police force, although theoretically Bannermen could be wearing this uniform as well. Those with 勇 would be the militia.
In most cases, 勇 would be of inferior quality to 兵. There is also a connotation of loyalty - as 勇 are raised by local authorities, they tend to be less loyal to the Imperial regime than their local masters. Things were different during and after the Taiping rebellion, where the 勇 were transformed into a standing army called the Xiang Army. The fact that these soldiers were - like their 勇 predecessors - loyal only to their own commanders would foreshadow the Warlord Era, where many of the warlord armies could trace their origins back to various Xiang armies.
Further information here: http://history.sina.com.cn/bk/mqs/2013-12-18/145264781.shtml