What is the significance of Saussure's theory of structuralism in this line? "De Saussure studied linguistics as a system of signs which can be...

Although Saussure did study historical linguistics, with his work Course in General Linguistics, he chose to focus on language synchronically. Whereas a diachronic analysis would look at how language changes over time, a synchronic analysis looks at how a language works at one moment in time. 

Saussure says that "langue" (the system and structure of language) persists as a whole while "parole" (speech) consists of each individual speaking (or writing). In other words, langue is the structure and rules of language in the same way that a game has structure and rules. Each person is therefore a player, and each move (parole) is the person participating in the game. 

Saussure uses the game of chess to illustrate these notions of langue and parole as they apply to a synchronic perspective on language. The rules and structure of chess exist abstractly, but they continue to be put into practice because people, as a society agree to play by those rules. This is the langue component. Each move in the game is an example of parole. Saussure claimed that one could come into a game at any point and he/she would not need to know the previous moves (diachronic) in order to understand the game. Therefore, he figured a synchronic approach to language would be equally logical.

Even without knowing the rules, one could eventually understand the interaction of the pieces in order to understand the game. Likewise, one can understand how language works (and means things) by how the words relate to each other. For example, Saussure noted that the word itself ("tree") is not what carries the meaning. Rather, meaning is determined by how "tree" and the idea (tree) that it signifies relates to and interacts with other words.