When linguists say that language is "rule-governed behavior," they mean it has a grammar, or a set of conventions that organizes its "proper" use. These rules set boundaries around the meaning of words and dictate how words relate to one other. In different languages, the rules vary in importance: for example, in English, word order is of supreme importantance in determining meaning; in Latin, however, word endings are more important.
Without rules (grammar), languages would quickly descend into chaos and meaninglessness. People would no longer be able to understand or communicate with each other. If the rules become too strict, however, they can stifle growth and creativity and make it difficult for subaltern groups in a society, who often have a distinct grammar or set of language rules, to advance or have an impact on their culture. Healthy languages evolve and live in an on-going tension between the current rules and pressures to change to conform to new social realities. Linguistics sometimes refer to how language is really used in culture, as the functional aspect of language, which, as noted before, exists in tension with the rules in textbooks. A current example of this would be the grammar guide prohibition on ending a sentence with a preposition versus the cultural tendency to do just that. As the function of a language changes, the rules, after a time, follow suit, which is why we no longer refer to our close friends as "thee" and "thou," but rather as "you."
"Language is rule-governed behavior" means essentially that language only works if we follow its rules. Language exists for the purpose of communication, meaning that we must first agree upon what words mean. This itself is a rule: We must use words to signify what others speaking the same language have agreed the words mean. For example, I cannot randomly decide that "desk" means "tree stump," ask you to place a glass on the desk, then get upset with you because you didn't put it on the tree stump.
Other rules we follow are those of syntax--the arrangement of words and phrases. In English, the arrangement of words in a sentence can alter its meaning, so we must observe the language's rules to effectively communicate. For example, if I mean, "Throw some hay over the fence to the cow," I cannot randomly rearrange this into "Throw the cow over the fence some hay" and expect you to understand me. Rules govern all of these arrangements.