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).