A reader of the MomsRising post below had asked how an increase to the minimum wage could posibbly cause unemployment, reasoning that a better-paid worker is a happy worker, leading to greater productivity and profit for the employer. That could be true if we only looked at the worker side of the equation, but let’s break it into that old economics standby, the supply/demand graph.
In the panels below, the amount of labor demanded by employers for a particular wage is represented in blue; the supply of labor willing to work for that given wage is shown in pink.
In the first graph, we see the wage equilibrium point, the point where demand for labor balances out with the available supply at a wage level acceptable to both sides.

When a minimum wage is set, it creates a binding price floor for wages. If the minimum wage is below the wage equilibrium point, then there is no effect on supply and demand for labor. However, in the second graph, a wage floor has been instituted that is above the wage equilibrium.

Point A, where the minimum wage crosses the labor demand line, creates a theoretical limit on the amount labor an employer will demand. (“Theoretical”, in that an employer could still hire more workers at the minimum wage rate, but that changes their demand curve.)
At point B, we see that workers will accept higher wages but do not have to accept lower, pretty much negating the lower part of their supply curve. The difference between points A & B is considered labor surplus, or ….unemployment. There is more labor available than employers are willing to pay for.
Not all workers might be affected. Those earning wages significantly higher than the minimum wage typically are not, but workers closer to the minimum usually feel the effects. More often than not, these are lower-skilled, lower-paid workers that the minimum wage was intended to help.
The net effect of raising the minimum wage is that while it might improve the wages of labor already in the workforce, and also raising the cost of labor for employers, it creates a barrier to entry of new workers who might have otherwise accepted wages lower than the minimum. These potential new workers, combined with workers who may have lost their jobs due to the increased cost of labor, are the unemployment that we’re concerned with.