You haven't put anything inside m <- c() in your loop since you did not use an assignment. You are getting the following -

m <- c()
m
# NULL

You can change the function to return the desired values by assigning m in the loop.

squared <- function(x) {
    m <- c()
    for(i in 1:x) {
        y <- i * i
        m <- c(m, y)
    }
    return(m)
}

squared(5)
# [1]  1  4  9 16 25

But this is inefficient because we know the length of the resulting vector will be 5 (or x). So we want to allocate the memory first before looping. This will be the better way to use the for() loop.

squared <- function(x) {
    m <- vector("integer", x)
    for(i in seq_len(x)) {
        m[i] <- i * i
    }
    m
}

squared(5)
# [1]  1  4  9 16 25 

Also notice that I have removed return() from the second function. It is not necessary there, so it can be removed. It's a matter of personal preference to leave it in this situation. Sometimes it will be necessary, like in if() statements for example.

I know the question is about looping, but I also must mention that this can be done more efficiently with seven characters using the primitive ^, like this

(1:5)^2
# [1]  1  4  9 16 25

^ is a primitive function, which means the code is written entirely in C and will be the most efficient of these three methods

`^`
# function (e1, e2)  .Primitive("^")