Here is an example that should demonstrate the difference

~$ t="alfa beta"

~$ if [ -n $t ] ; then echo OK ; fi 

 bash: [: alfa: binary operator expected

~$ if [ -n "$t" ] ; then echo OK ; fi 

 OK

~$ ls blah*

blah1 blah2 blah3

~$ t="blah*"

~$ if [ -n "$t" ] ; then echo OK ; fi 

 OK

~$ if [ -n $t ] ; then echo OK ; fi

bash: [: too many arguments

In other words, with quotes, the $t is expanded only once and put in quotes as a single argument to test ([ is just an alias to test). Without quotes, it is substituted by the contents of $t and then expanded again.