A standard idea in economic theory that there is a fixed amount of work in an economy to be divided up among the total supply of laborers, instead of a quantity that changes with the economic climate. This a term in standard economic theory, developed as an answer to two common policies that governments sometimes use to address unemployment.
The first is shortening the work week to "create" jobs. When unemployment is high, governments sometimes legislate a shortened work week or impose a cap on the number of hours workers can work. The idea is to "divide up the labor" evenly among available workers, and thus create more jobs.
The second involves protectionism and labor migration. A standard argument for protectionism is that markets or industries need protection from foreign markets that are more efficient or have lower labor costs, e.g., "our jobs are going overseas".
The lump-of-labor fallacy says that these are based on faulty reasoning, since the amount of available work is not fixed: new jobs are created or disappear based on the cost of labor (wages), the cost of money (exchange rates and interest rates), innovation, and other economic variables. In particular, the labor picture evolves with structural changes in the economy, e.g. the transition from a goods-based to a service-based economy.
It should be noted that this idea is somewhat controversial because it hinges on several standard economic assumptions, especially the mobility of labor and capital. A large factory in a small town that closes to move overseas creates a real loss of jobs that can be devastating to workers in the short term. The theory assumes that in the long run the displaced workers will either move to other areas where there are jobs, or that new employers will move in to take advantage of the increased labor pool.