Restrictive clauses limit or define the noun they modify and are essential to meaning: "The student who finished first won a prize" (which student? the one who finished first). Nonrestrictive clauses add extra information about an already-identified noun and are set off by commas: "Maria, who finished first, won a prize" (Maria is identified; the clause adds information).
Test whether the clause is essential by removing it. If removing it changes the meaning significantly, it's restrictive (no commas). If the noun is already clear and the clause merely adds extra information, it's nonrestrictive (use commas).
You have learned how relative clauses work: they modify nouns, are introduced by relative pronouns, and add information about the noun they follow. Now consider a critical question those lessons left open: when does a relative clause identify *which* noun you mean, and when does it merely provide additional information about a noun already identified? This distinction — between restrictive and nonrestrictive relative clauses — determines both meaning and punctuation.
A restrictive clause restricts the reference of the noun — it narrows down which particular instance you mean from a larger set. "The student who finished first won a prize" is not about students in general; it is about a specific one, identified by the clause "who finished first." Remove the clause and you don't just lose information — you lose identification: "The student won a prize" becomes a different sentence that leaves the reader asking "which student?" The clause is essential to the meaning. Restrictive clauses are written without commas because they are integrated into the noun phrase.
A nonrestrictive clause adds supplementary information about a noun already uniquely identified. "Maria, who finished first, won a prize" — Maria is identified by name before the clause begins. The clause "who finished first" adds a fact but is not needed to know who we are talking about. Remove it and you lose a detail, not the identity: "Maria won a prize" refers to the same person. Nonrestrictive clauses are set off by commas because they are parenthetical — information the sentence could do without.
The comma difference carries real meaning stakes. "The professors who supported the proposal were rewarded" (restrictive) implies that some professors did not support it — only the ones who did were rewarded. "The professors, who supported the proposal, were rewarded" (nonrestrictive) implies all professors supported it, with the clause noting that in passing. Same words, two different commas, two different factual claims. A reliable test: read the sentence without the clause. If the noun's reference is still clear, the clause is nonrestrictive — use commas. If the noun now floats unanchored, the clause is restrictive — omit the commas.