What does the function invisible() do?

From ?invisible:

Details:

 This function can be useful when it is desired to have functions
 return values which can be assigned, but which do not print when
 they are not assigned.

So you can assign the result, but it will not be printed if not assigned. It's often used in place of return. Your print.myPrint method only prints because you explicitly call print. The call to invisible(x) at the end of your function simply returns a copy of x.

If you didn't use invisible, x would also be printed if not assigned. For example:

R> print.myPrint <- function(x, ...){
+   print(unlist(x[1:2]))
+   return(x)
+ }
R> print(x)
v11 v12 v13 v14 v15 v21 v22 v23 v24 v25 
  1   2   3   4   5  -1  -2  -3  -4  -5 
v11 v12 v13 v14 v15 v21 v22 v23 v24 v25 
  1   2   3   4   5  -1  -2  -3  -4  -5 

While invisible() makes its content temporary invisible and is often used instead of return() it should rather be used in combination with return() and not as its replacement.

While return() will stop function execution and return the value put into it, invisible() will do no such thing. It only makes its content invisible for a while.

Consider the following two examples:

f1 <- function(x){
  if( x > 0 ){
     invisible("bigger than 0")
  }else{
     return("negative number")
  }
  "something went wrong"
}

result <- f1(1)

result
## [1] "something went wrong"



f2 <- function(x){
  if( x > 0 ){
     return(invisible("bigger than 0"))
  }else{
     return("negative number")
  }
}

result <- f2(1)

result
## [1] "bigger than 0"

Having circumvented invisible()'s pitfall we can have a look at its working:

f2(1)

The function does not print its return value due to the use of invisible(). It does however pass on the value as usual:

res <- f2(1)
res 
## [1] "bigger than 0"

invisible()'s use cases are e.g. to prevent function return values that would produce page after page of output or when a function is called for its side effect and the return value is e.g. only used to give further information ...

This excerpt from the Tidyverse Design Guide book explains why it might be useful to return an invisible value.

If a function is called primarily for its side-effects, it should invisibly return a useful output. If there’s no obvious output, return the first argument. This makes it possible to use the function with in a pipeline.

https://design.tidyverse.org/out-invisible.html