To help newbies navigate through the manual fog, it might be helpful to see the [[ ... ]]
notation as a collapsing function - in other words, it is when you just want to 'get the data' from a named vector, list or data frame. It is good to do this if you want to use data from these objects for calculations. These simple examples will illustrate.
(x <- c(x=1, y=2)); x[1]; x[[1]]
(x <- list(x=1, y=2, z=3)); x[1]; x[[1]]
(x <- data.frame(x=1, y=2, z=3)); x[1]; x[[1]]
So from the third example:
> 2 * x[1]
x
1 2
> 2 * x[[1]]
[1] 2