ag.algebraic geometry - The meaning of ${infty}^{k}$.

When we say, that, say, a surface contains ${infty}^{k}$ lines, do we mean that it contains a k-parameter family of lines? Do we assume that this family is parametrized by a $P^{k}$, say, or we use this term more informally?
This is certainly a standard notation, but I didn't see its explanation in standard modern textbooks.