What do the . and .. directories represent in Linux?

. means "this directory" and .. means "the directory one level up" — they're real entries present in every directory, not just typing shortcuts.

This is more literal than it looks. Every directory on disk physically contains two hidden entries, . pointing at itself and .. pointing at its parent. Run ls -a anywhere and you'll see them. That's how the shell can walk up the tree at all: .. is the recorded link back to the parent.

./script.sh   # run script.sh sitting in the current directory
cd ..         # move up one level
cd ../..      # move up two levels
cp file.txt . # copy file.txt into here
ls ..         # list the parent's contents

Why you must write ./script.sh and not just script.sh: for security, the shell does not search your current directory for programs by default — it only looks in the directories listed in $PATH. If a malicious file named ls sat in a shared folder, you wouldn't want it run just because you typed ls. The explicit ./ says "yes, run this local file on purpose."

Tip: Because . is a real entry, cp something . and mv something . are the idiomatic way to say "drop it right here" without typing the full path.