Why would an increase in the productivity of labor lead to an increase or a decrease in the demand for labor?
All other things being equal, an increase in the productivity of labor would lead to a decline in the demand for that labor. This is because an increase in productivity means that the same amount of output can now be produced by a smaller number of workers.
Productivity can be defined as the amount of a good that can be produced by one person in a given amount of time. When productivity goes up, each worker can make more units of a good in a day or in any other time period. This means that an increase in productivity leads to a decrease in the demand for labor (all other things being equal).
Let us imagine that you have a taco truck and you need to make 100 tacos per hour. If your workers can make 34 tacos per hour, you need three workers. But not imagine some advance allows your workers to make 50 tacos per hour. They are more productive, but now you need fewer of them because two of them can make the number of tacos that used to require three workers.
Thus, an increase in productivity will lead to a decrease for demand for labor if all other things remain equal.