In order for a direct producer to perform surplus labor, then four conditions must first be met:  1. She must create products with social value.  2. This value is affirmed by the existence of demand for that product, i.e. someone expresses a desire to make use of the product, typically by offering to buy it in a market exchange. We describe the relative value of a product by reference to its market value (or exchange value).  3. The compensation received by the direct producer for her work has value less than the total value of her creations.  4. This compensation plus the value of used up raw materials and the wear and tear on machinery and tools is also less than the total value of her creations. The excess value above the value of the worker's compensation plus the value of used up materials and machinery is surplus value. Surplus labor is that labor performed in the creation of this surplus value. The existence of surplus labor/value is affirmed by the distribution of direct labor, products, or some other form of this excess value (such as in monetary form) to economic agents who do not participate in the production of that value, such as the payment of taxes to the state or the payment of merchant's fees or the payment of salaries to overseers. 
Neoclassical economic theory was developed, in part, to attack the very notion of surplus labor or surplus value and to argue that workers receive all of the value embodied in their creative efforts. In other words, the theory had a clear ideological purpose that shaped the underlying theoretical framework. The same can be said of the Marxian theory that neoclassical theory attacked. Marxian theory argued for the existence of surplus labor, in part, to lay the groundwork for a criticism of class societies, including capitalist societies. If workers perform surplus labor in capitalism, then the surplus labor is taken from them by the capitalist board of directors. Capitalism would then represent a form of theft. The neoclassical theorists went for the Marxian jugular, so to speak, by arguing against the very existence of surplus labor or surplus value. In the neoclassical world, there is no exploitation in capitalism because in capitalism workers bargain for their wages in a free market where all economic agents are equal. The result is that workers will be hired/will agree to work only up to the point where there is no surplus value/labor (wage=value of the marginal physical product). If there is no surplus labor, then workers are not exploited (since exploitation is defined as pushing workers/direct producers to perform surplus labor). If there is no exploitation then capitalism is not a form of theft and, by extension, not morally wrong. 
We have seen that the labourer,
during one portion of the labour-process,
produces only the value of his labour-power . . .
The portion of his day's labour
devoted to this purpose,
will be greater or less,
in proportion to the value
of the necessaries that he daily requires
on an average, or, equivalently,
in proportion to the labour-time required
on an average to produce them.
During the second period of the labour-process,
that in which his labour is no longer necessary labour,
the workman, it is true, labours, expends labour-power;
but his labour, being no longer necessary labour,
he creates no value for himself.
He creates surplus-value
which, for the capitalist,
has all the charms of a creation out of nothing.
This portion of the working-day,
for a definite period of time,

I name surplus labour-time,
and to the labour expended during that time,
I give the name of surplus-labour.

---Marx, from Capital, Vol. 1



The class process is that (process)

"in which unpaid surplus-labour is pumped

out of direct producers . . ."

To clarify the definition of class

as a particular social process

requires that Marx specify what he means

by surplus labor.

He does this by his often-repeated

distinction between necessary and surplus labor.

The former is the quantity of labor time

necessary to produce the consumables

customarily required by the direct producer

to keep working.

Surplus labor then is the further,

the extra time of labor

the direct producer performs beyond

the necessary labor.

Necessary and surplus are historically

variable quantities:

they are overdetermined.

---Resnick and Wolff, Knowledge and Class, University of Chicago Press, 1987, p. 115.