Reserve army of labour is a concept in Karl Marx's critique of political economy. It refers to the unemployed and underemployed in capitalist society. It is synonymous with "industrial reserve army" or "relative surplus population", except that the unemployed can be defined as those actually looking for work and that the relative surplus population also includes people unable to work. The use of the word "army" refers to the workers being conscripted and regimented in the workplace in a hierarchy under the command or authority of the owners of capital.
Marx did not invent the term "reserve army of labour". It was already being used by Friedrich Engels in his 1845 book The Condition of the Working Class in England. What Marx did was theorize the reserve army of labour as a necessary part of the capitalist organization of work.