There ought to be a space between : and the $.
Anyways, what it does it checks for the existence of a variable called dummy_msg. If it does not exist (not defined) or is empty, it will set the value of the same as 'Nothing started'.
Consider this:
nilesh@Linux ~ $ set | grep dummy
nilesh@Linux ~ $ : ${dummy_msg:="Nothing started."}
nilesh@Linux ~ $ set | grep dummy
dummy_msg='Nothing started.'
nilesh@Linux ~ $ dummy_msg=
nilesh@Linux ~ $ set | grep dummy
dummy_msg=
nilesh@Linux ~ $ : ${dummy_msg:="Nothing started."}
nilesh@Linux ~ $ set | grep dummy
dummy_msg='Nothing started.'