Let's begin by defining “system.” According to Merriam-Webster, a system is a group of objects, ideas, principles, or elements that work together for a common purpose. It is an organized network or arrangement that carries out a particular function. When we say that language is a system, then, we mean that it involves a group of elements working together to serve a purpose—namely, communication.

Language, however, is made up not just of individual elements, but actually of several subsystems. Each of these systems contains an organized network of elements in its own right—elements that work together to serve a purpose and accomplish an objective. Linguists identify several subsystems of language, including phonology, morphology, lexicology, syntax, semantics, and pragmatics. We'll look briefly at each of these.

Phonology is all about the sounds of a language and how they are combined and organized into meaningful strings. Linguists that study phonology will be interested in why vowels make different sounds in different words, for instance. Morphology studies how words are built from morphemes (units of meaning). Scholars interested in morphology will identify various grammatical structures and how they combine to make meaning (like -ed or -ing being used to form the verbal past tense and participle, for example).

Lexicology pays attention to forms, meanings, and uses of words as well as their development and history. Syntax studies how words are formed into phrases and sentences and why they are structured and ordered the way they are (why subjects usually precede verbs in English, for instance). Semantics is all about the meanings that are expressed through words and syntax. Pragmatics looks at how language is used in context and how meanings can vary or be revealed or concealed according to a speaker's situation.

These systems, then, combine to make the larger system we call language.

As another Educator has already noted, the notion that language is a “system of systems” stems from an academic article published by J. W. F Mulder and S. G. J. Hervey in the 1970s. Their article is appropriately titled “Language as a System of Systems.” It investigates the mini networks (“systems”) that comprise the larger network (“system”) of language.

Someone might note that Mulder and Hervey’s meticulous breakdown of language is not so dissimilar from deconstructionism. While Mulder and Hervey take apart language as a whole in order to highlight its various elements, deconstructionists take apart a specific language—the language used in a particular book—in order to demonstrate how the meaning of that book, and the language within, is dependent on a host of varying systems. In both instances, it’s noteworthy that language comes off as constantly vulnerable to dissection.

Someone might also note how the phrase indicates that language doesn’t function in a vacuum. While language might contain many systems, it's also a part of many other systems, including economic systems, environmental systems, biological systems, and so on.

For example, the way that people use the system of language to discuss the economic system impacts who makes money and who receives money.

Independent senator Bernie Sanders recently used the system of language to make the case that people should receive more than $600 as a part of a COVID-19 relief package. Republican senator Mitch McConnell, meanwhile, used the system of language to criticize Sanders for preventing the military from receiving more money. This example shows how the system of language functions in another system: politics.

We talk about language as a "system of systems" because it consists of interdependent systems that only become fully meaningful when combined. We cannot think of spoken language without phonology, the individual sounds that make up words, but these sounds would be meaningless if they did not correspond to words that we understand as meaningful. Similarly, language would be incredibly limited if we had words but no way to pronounce them.

In order for language to work, we need a way to say words (phonology), meaning attached to these words (morphology), an understanding of the meanings of words combine within a sentence (syntax), and an understanding of how greater, non-verbal context informs of the meaning of language (pragmatics). While it is easy to think of language as simple and automatic if you are fluent in a language, there are many different systems that all work in conjunction to give this effect. This is especially clear if you ever try to learn a new language and realize how many different pieces you have to learn before you can easily navigate the language.

Language is considered as a system primarily because it is made of linguistic units that are interdependent of each other. Since they are smaller units working within a whole system, by default, language becomes a system of systems. The basic premise of this concept is that the diversity of features that are found in language formation and production prevents it from being described in a diluted or generalized way. Instead, language study has to be pulled apart and studied by each of its multifunctional sub-systems. 

The idea of language being a system of systems comes primarily from an article written by Mulder and Hervey (1975) and publishedLa Linguistique(11,(2)). Mulder and Hervey's definition of language follows a functionalist perspective in which language is defined as a "genus" and, as such, it should be subdivided into a smaller sub-parts, or systems. 

Five sub-systems of language are identified as 

1. Semantics- Rules of language content. It has a sub-system of its own based on vocabulary and word localization. 
2. Pragmatics- Rules of language usage (function and appropriateness)
3. Syntax- Rules for word order and arrangements
4. Morphology- Rules for word formation. Also has its own sub-system of morphemes. 
5. Phonology- Rules for how the language sounds, or should sound. 

Therefore, the complexity of language and the fact that it is a composite of various functional parts are the conditions that deem it, quite correctly, as a system of systems.