Pass space separated arguments stored in variable to command

As long as this is a bash script (or even most versions of sh) you should use an array to pass arguments rather than a variable:

DIRS=('/home/' '/var/www/html' '/etc')

tar -czf /backup/file.tar.gz "${DIRS[@]}"

This can be written as follows if you prefer (usually easier to read if the array gets large):

DIRS=(
    '/home/' 
    '/var/www/html' 
    '/etc'
)

---

In a shell that does not support arrays you will need to unquote your variable to allow word splitting (Not recommended if it can be avoided):

DIRS="/home/ /var/www/html /etc"

tar -czf /backup/file.tar.gz ${DIRS}

---

When you quote the variable to pass these arguments it's essentially the same as:

tar -czf /backup/file.tar.gz "/home/ /var/www/html /etc"

However when you pass them through a quoted array it will be more like:

tar -czf /backup/file.tar.gz "/home/" "/var/www/html" "/etc"

Passing them through an unquoted array or variable will perform somthing similar to:

tar -czf /backup/file.tar.gz /home/ /var/www/html /etc

Which in this example should not be an issue but leaves it open to additional word splitting and other types of expansion that may be undesirable or potentially harmful.