The mutate() function in R adds new columns to a data frame by calculating values from existing columns. It takes the data frame and new column definitions, computes the values row by row, and returns a new data frame with the added columns. You must assign the result back to a variable to keep the changes. For example, mutate(data, z = x + y) adds a column z that sums x and y. The execution table shows each step: starting with the original data, calculating z, adding z to the data frame, and returning the updated data. Variable tracking shows how the new column z changes from not existing to having values. Remember, mutate does not change the original data frame unless you assign the result back.