What does this quote by Chomsky mean?

Question

“Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied.”

Answer 1

I suppose the first question is, what do you mean by "mean"? I assume you are asking about his communicative intent in the text, which part of a talk given at Loyola University (Chicago), January 8–9, 1970 at a political symposium on Freedom and Human Sciences. The full text can be seen here, and was apparently published originally in For reasons of state. The full paragraph reads:

A similar concept of human nature underlies Humboldt’s work on language. Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied. Even the interpretation and use of words involves a process of free creation. The normal use of language and the acquisition of language depend on what Humboldt calls the fixed form of language, a system of generative processes that is rooted in the nature of the human mind and constrains but does not determine the free creations of normal intelligence or, at a higher and more original level, of the great writer or thinker. Humboldt is, on the one hand, a Platonist who insists that learning is a kind of reminiscence, in which the mind, stimulated by experience, draws from its own internal resources and follows a path that it itself determines; and he is also a romantic, attuned to cultural variety, and the endless possibilities for the spiritual contributions of the creative genius. There is no contradiction in this, any more than there is a contradiction in the insistence of aesthetic theory that individual works of genius are constrained by principle and rule. The normal, creative use of language, which to the Cartesian rationalist is the best index of the existence of another mind, presupposes a system of rules and generative principles of a sort that the rationalist grammarians attempted, with some success, to determine and make explicit.

The immediately following paragraph helps to contextualize what he is going on about:

The many modern critics who sense an inconsistency in the belief that free creation takes place within – presupposes, in fact – a system of constraints and governing principles are quite mistaken; unless, of course, they speak of “contradiction” in the loose and metaphoric sense of Schelling, when he writes that “without the contradiction of necessity and freedom not only philosophy but every nobler ambition of the spirit would sink to that death which is peculiar to those sciences in which that contradiction serves no function.” Without this tension between necessity and freedom, rule and choice, there can be no creativity, no communication, no meaningful acts at all.

The fundamental problem for Chomsky is to resolve the contradiction between his political view that people should be free, espousing a libertarian socialist viewpoint, whereas people are biologically precluded from enjoying "full freedom" because of the automatic and highly restricted nature of the language faculty, in his view.

He further attempts to make a connection between language and freedom in an earlier paragraph, declaring that

Were we to combine these speculations, we might develop an interesting connection between language and freedom. Language, in its essential properties and the manner of its use, provides the basic criterion for determining that another organism is a being with a human mind and the human capacity for free thought and self-expression, and with the essential human need for freedom from the external constraints of repressive authority. Furthermore, we might try to proceed from the detailed investigation of language and its use to a deeper and more specific understanding of the human mind

The point of the essay is to give one the feeling that one can still be politically free despite have a highly restrictive formal mechanism for constructing linguistic utterances.

Answer 2

“Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied.“

It means,

language is “creative”

Language is a system that can create, construct, or generate sentences/expressions/elements. Under a loose interpretation, you could say there are systems in nature which have more or less creative capability, the ability to create new or unique things. It may be the case that beaver dams have continuous variation in some parameters but in others have very similar reproduced form (I don’t know). But plants, for example, may have an infinitude of unique structures (the ones that are more mathematical or fractalian, like ferns). Simply put, there is a system in nature, like a geyser, or a cloud, or a mushroom, that appears to “produce” something, a spout of water, a whale song, the way fungi germinate / release spores, the water water flows in rivers, patterns of snowfall, flocks of birds, the structure of ice crystals, the color patterns in geological sediment, the structure of dinosaur bones, the distribution of stars in the sky, etc. There is some distinction between substrate and substance - what vessel enables a phenomenon to arise - and what is that phenomenon (even if a virtual pattern or structure) like?

language is “free” and “infinite”

Pretty much, that language possesses the property of infinitude, unless some other systems. Chomsky believes that the mathematical operations that create language structures are recursive in a particular sense. They can take an element they generated, and use it again to construct another new element. Exactly like a recursive mathematical function that keeps making new elements in a sequence. As a matter of fact, mathematics can be founded / defined in terms of set theory, and one can specify what sets exist through a recursive function, like the Von Neumann hierarchy, in which you create new sets, by taking subsets of sets you already have: this goes on forever and creates infinitely more unique sets that never run out of new possible sets.