Explaining this command means explaining regular expressions, something that people have literally written whole books about.
In a nutshell $var is a variable I'd assume is the root directory you're looking to get a tree mapping of.
ls -R is listing every directory tree recursively, it then grabs all the lines that end in
: aka all directory lines
The sed commands edit the streams to produce the file-tree look of the result. It replaces the first expression with the second, so:
sed 's/this/that/' will replace all occurences of 'this' with 'that'.
It is
MUCH more complex than this. The details of sed could fill another book, volume two of the regular expressions anthology.
You can ultimately get all the same info just using
ls -R $var | grep ":$", all the other commands just make it look prettier.
If you want to learn more about sed and regular expressions there is a lot of good info online. Here is a good tutorial:
http://www.grymoire.com/Unix/index.html
