This lesson shows how to access columns in R data frames using $ and [] operators. Starting with a data frame, you can extract a column as a vector using df$col or df[["col"]]. Using df["col"] extracts the column but keeps it as a data frame with one column. The execution table traces creating a data frame, extracting the 'age' column as a vector and as a data frame, and checking their types. Key moments clarify why $ returns a vector and ["col"] returns a data frame. The quiz tests understanding of these differences. Remember, use $ or [[ ]] for vectors, and [ ] for data frames.