How to cd into a directory with space in the name?

$ cd "$DOCS"

You need to quote "$DOCS" to prevent spaces from being parsed as word separators. More often than not, variable references should be quoted.

Note that $HOME would have the same problem. The issue is coming from when the shell evaluates variable references; it's nothing to do with what variables you use or how you assign to them. It's the expansion that needs to be quoted.

$ echo $HOME
/home/my dir

This is deceptive. echo is actually echoing the two strings /home/my and dir. If you use cd or ls you'll see how it's actually working.

$ ls $HOME
ls: cannot access /home/my: No such file or directory
ls: cannot access dir: No such file or directory
$ cd $HOME
bash: cd: /home/my: No such file or directory
$ cd "$HOME"
<success!>

---

Can I ask why it works when I manually type it in but not in a variable?

Great question! Let's examine the commands you typed:

$ DOCS="\"/cygdrive/c/Users/my dir/Documents\""
$ echo $DOCS
"/cygdrive/c/Users/my dir/Documents"
$ cd $DOCS
-bash: cd: "/cygdrive/c/Users/my: No such file or directory

The reason this doesn't work is because Bash doesn't parse quotes inside variable expansions. It does perform word splitting, so whitespace in unquoted variable expansions is taken as word separators. It doesn't parse quotes in any way, meaning you can't put double quotes inside a variable to override word splitting.

$ cd $DOCS

Because of this, cd is passed two parameters. As far as cd knows it looks like you wrote:

$ cd '"/cygdrive/c/Users/my' 'dir/Documents"'

Two parameters, with double quotes intact.

SOLUTION:

cd "Documents and Photos"

problem solved.

The reason I'm submitting this answer is you'll find that StackOverflow is being used by every day users (not just web devs, programmers or power users) and this was the number one result for a simple Windows user question on Google.

People are becoming more tech-savvy, but aren't necessarily familiar with command line in the cases above.