I’m guessing what this means is that if $C$ is the cost function and $x$ represents the number of units of a good produced, marginal cost at production level $x_0$ is not the cost of producing the $(x_0)$th unit. And, importantly, if goods are not sold in discrete amounts, it’s not quite the cost of producing the next “unit” either.

If the goods sold in discrete amounts (that is, if $x \in \mathbb{N}$), then marginal cost at production level $x_0$ is defined as $C(x_{0}+1) - C(x_0)$. For example, marginal cost when $15$ goods have been produced is the additional cost of producing the $16$th good, not the $15$th good.

More often than not, though, economists assume the good is continuous (e.g., milk, for instance). In that case, marginal cost at production level $x_0$ is the derivative of the cost function at $x = x_0$, i.e., $C'(x_0)$. That means it's the cost of producing an additional incremental amount of the good (i.e., the “instantaneous rate of change” of the cost with respect to quantity).

I’m guessing what this means is that if $C$ is the cost function and $x$ represents the number of units of a good produced, marginal cost at production level $x_0$ is not the cost of producing the $(x_0)$th unit. And, importantly, if goods are not sold in discrete amounts, it’s not quite the cost of producing the next “unit” either.

If the good is produced in discrete amounts (that is, if $x \in \mathbb{N}$), then marginal cost at production level $x_0$ is defined as $C(x_{0}+1) - C(x_0)$. For example, marginal cost when $15$ goods have been produced is the additional cost of producing the $16$th good, not the $15$th good.

More often than not, though, economists assume the good is continuous (e.g., milk, for instance). In that case, marginal cost at production level $x_0$ is the derivative of the cost function at $x = x_0$, i.e., $C'(x_0)$. That means it's the cost of producing an additional incremental amount of the good (i.e., the “instantaneous rate of change” of the cost with respect to quantity).